TY - CONF
AB - Games on graphs provide the appropriate framework to study several central problems in computer science, such as verification and synthesis of reactive systems. One of the most basic objectives for games on graphs is the liveness (or Büchi) objective that given a target set of vertices requires that some vertex in the target set is visited infinitely often. We study generalized Büchi objectives (i.e., conjunction of liveness objectives), and implications between two generalized Büchi objectives (known as GR(1) objectives), that arise in numerous applications in computer-aided verification. We present improved algorithms and conditional super-linear lower bounds based on widely believed assumptions about the complexity of (A1) combinatorial Boolean matrix multiplication and (A2) CNF-SAT. We consider graph games with n vertices, m edges, and generalized Büchi objectives with k conjunctions. First, we present an algorithm with running time O(k*n^2), improving the previously known O(k*n*m) and O(k^2*n^2) worst-case bounds. Our algorithm is optimal for dense graphs under (A1). Second, we show that the basic algorithm for the problem is optimal for sparse graphs when the target sets have constant size under (A2). Finally, we consider GR(1) objectives, with k_1 conjunctions in the antecedent and k_2 conjunctions in the consequent, and present an O(k_1 k_2 n^{2.5})-time algorithm, improving the previously known O(k_1*k_2*n*m)-time algorithm for m > n^{1.5}.
AU - Chatterjee, Krishnendu
AU - Dvorák, Wolfgang
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 1068
TI - Conditionally optimal algorithms for generalized Büchi Games
VL - 58
ER -
TY - CONF
AB - The Continuous Skolem Problem asks whether a real-valued function satisfying a linear differen-
tial equation has a zero in a given interval of real numbers. This is a fundamental reachability
problem for continuous linear dynamical systems, such as linear hybrid automata and continuous-
time Markov chains. Decidability of the problem is currently open – indeed decidability is open
even for the sub-problem in which a zero is sought in a bounded interval. In this paper we show
decidability of the bounded problem subject to Schanuel’s Conjecture, a unifying conjecture in
transcendental number theory. We furthermore analyse the unbounded problem in terms of the
frequencies of the differential equation, that is, the imaginary parts of the characteristic roots.
We show that the unbounded problem can be reduced to the bounded problem if there is at most
one rationally linearly independent frequency, or if there are two rationally linearly independent
frequencies and all characteristic roots are simple. We complete the picture by showing that de-
cidability of the unbounded problem in the case of two (or more) rationally linearly independent
frequencies would entail a major new effectiveness result in Diophantine approximation, namely
computability of the Diophantine-approximation types of all real algebraic numbers.
AU - Chonev, Ventsislav K
AU - Ouaknine, Joël
AU - Worrell, James
ID - 1069
TI - On the skolem problem for continuous linear dynamical systems
VL - 55
ER -
TY - CONF
AB - We present a logic that extends CTL (Computation Tree Logic) with operators that express synchronization properties. A property is synchronized in a system if it holds in all paths of a certain length. The new logic is obtained by using the same path quantifiers and temporal operators as in CTL, but allowing a different order of the quantifiers. This small syntactic variation induces a logic that can express non-regular properties for which known extensions of MSO with equality of path length are undecidable. We show that our variant of CTL is decidable and that the model-checking problem is in Delta_3^P = P^{NP^NP}, and is DP-hard. We analogously consider quantifier exchange in extensions of CTL, and we present operators defined using basic operators of CTL* that express the occurrence of infinitely many synchronization points. We show that the model-checking problem remains in Delta_3^P. The distinguishing power of CTL and of our new logic coincide if the Next operator is allowed in the logics, thus the classical bisimulation quotient can be used for state-space reduction before model checking.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 1070
TI - Computation tree logic for synchronization properties
VL - 55
ER -
TY - CONF
AB - We consider data-structures for answering reachability and distance queries on constant-treewidth graphs with n nodes, on the standard RAM computational model with wordsize W=Theta(log n). Our first contribution is a data-structure that after O(n) preprocessing time, allows (1) pair reachability queries in O(1) time; and (2) single-source reachability queries in O(n/log n) time. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries. The data-structure uses at all times O(n) space. Our second contribution is a space-time tradeoff data-structure for distance queries. For any epsilon in [1/2,1], we provide a data-structure with polynomial preprocessing time that allows pair queries in O(n^{1-\epsilon} alpha(n)) time, where alpha is the inverse of the Ackermann function, and at all times uses O(n^epsilon) space. The input graph G is not considered in the space complexity.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 1071
TI - Optimal reachability and a space time tradeoff for distance queries in constant treewidth graphs
VL - 57
ER -
TY - CONF
AB - While weighted automata provide a natural framework to express quantitative properties, many basic properties like average response time cannot be expressed with weighted automata. Nested weighted automata extend weighted automata and consist of a master automaton and a set of slave automata that are invoked by the master automaton. Nested weighted automata are strictly more expressive than weighted automata (e.g., average response time can be expressed with nested weighted automata), but the basic decision questions have higher complexity (e.g., for deterministic automata, the emptiness question for nested weighted automata is PSPACE-hard, whereas the corresponding complexity for weighted automata is PTIME). We consider a natural subclass of nested weighted automata where at any point at most a bounded number k of slave automata can be active. We focus on automata whose master value function is the limit average. We show that these nested weighted automata with bounded width are strictly more expressive than weighted automata (e.g., average response time with no overlapping requests can be expressed with bound k=1, but not with non-nested weighted automata). We show that the complexity of the basic decision problems (i.e., emptiness and universality) for the subclass with k constant matches the complexity for weighted automata. Moreover, when k is part of the input given in unary we establish PSPACE-completeness.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 1090
TI - Nested weighted limit-average automata of bounded width
VL - 58
ER -
TY - CONF
AB - We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results.
AU - Daca, Przemyslaw
AU - Henzinger, Thomas A
AU - Kretinsky, Jan
AU - Petrov, Tatjana
ID - 1093
TI - Linear distances between Markov chains
VL - 59
ER -
TY - CONF
AB - Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of quantitative functions, we establish that automata with monitor counters and nested weighted automata are equivalent. We study for the first time such quantitative automata under probabilistic semantics. We show that several problems that are undecidable for the classical questions of emptiness and universality become decidable under the probabilistic semantics. We present a complete picture of decidability for such automata, and even an almost-complete picture of computational complexity, for the probabilistic questions we consider. © 2016 ACM.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 1138
T2 - Proceedings of the 31st Annual ACM/IEEE Symposium
TI - Quantitative automata under probabilistic semantics
ER -
TY - CONF
AB - Given a model of a system and an objective, the model-checking question asks whether the model satisfies the objective. We study polynomial-time problems in two classical models, graphs and Markov Decision Processes (MDPs), with respect to several fundamental -regular objectives, e.g., Rabin and Streett objectives. For many of these problems the best-known upper bounds are quadratic or cubic, yet no super-linear lower bounds are known. In this work our contributions are two-fold: First, we present several improved algorithms, and second, we present the first conditional super-linear lower bounds based on widely believed assumptions about the complexity of CNF-SAT and combinatorial Boolean matrix multiplication. A separation result for two models with respect to an objective means a conditional lower bound for one model that is strictly higher than the existing upper bound for the other model, and similarly for two objectives with respect to a model. Our results establish the following separation results: (1) A separation of models (graphs and MDPs) for disjunctive queries of reachability and Büchi objectives. (2) Two kinds of separations of objectives, both for graphs and MDPs, namely, (2a) the separation of dual objectives such as Streett/Rabin objectives, and (2b) the separation of conjunction and disjunction of multiple objectives of the same type such as safety, Büchi, and coBüchi. In summary, our results establish the first model and objective separation results for graphs and MDPs for various classical -regular objectives. Quite strikingly, we establish conditional lower bounds for the disjunction of objectives that are strictly higher than the existing upper bounds for the conjunction of the same objectives. © 2016 ACM.
AU - Chatterjee, Krishnendu
AU - Dvoák, Wolfgang
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 1140
T2 - Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science
TI - Model and objective separation with conditional lower bounds disjunction is harder than conjunction
ER -
TY - CONF
AB - POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIMEcomplete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach. © 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Davies, Jessica
ID - 1166
T2 - Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence
TI - A symbolic SAT based algorithm for almost sure reachability with small strategies in pomdps
VL - 2016
ER -
TY - CONF
AB - Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decisionmaking and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning probability for a distinguished player, has received a lot of attention. Previous works consider the problem where the pairwise winning probabilities are known precisely, while we study how robust is the winning probability with respect to small errors in the pairwise winning probabilities. First, we present several illuminating examples to establish: (a) there exist deterministic tournaments (where the pairwise winning probabilities are 0 or 1) where one optimal draw is much more robust than the other; and (b) in general, there exist tournaments with slightly suboptimal draws that are more robust than all the optimal draws. The above examples motivate the study of the computational problem of robust draws that guarantee a specified winning probability. Second, we present a polynomial-time algorithm for approximating the robustness of a draw for sufficiently small errors in pairwise winning probabilities, and obtain that the stated computational problem is NP-complete. We also show that two natural cases of deterministic tournaments where the optimal draw could be computed in polynomial time also admit polynomial-time algorithms to compute robust optimal draws.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Tkadlec, Josef
ID - 1182
TI - Robust draws in balanced knockout tournaments
VL - 2016-January
ER -
TY - JOUR
AU - Hilbe, Christian
AU - Traulsen, Arne
ID - 1200
JF - Physics of Life Reviews
TI - Only the combination of mathematics and agent based simulations can leverage the full potential of evolutionary modeling: Comment on “Evolutionary game theory using agent-based methods” by C. Adami, J. Schossau and A. Hintze
VL - 19
ER -
TY - CONF
AB - To facilitate collaboration in massive online classrooms, instructors must make many decisions. For instance, the following parameters need to be decided when designing a peer-feedback system where students review each others' essays: the number of students each student must provide feedback to, an algorithm to map feedback providers to receivers, constraints that ensure students do not become free-riders (receiving feedback but not providing it), the best times to receive feedback to improve learning etc. While instructors can answer these questions by running experiments or invoking past experience, game-theoretic models with data from online learning platforms can identify better initial designs for further improvements. As an example, we explore the design space of a peer feedback system by modeling it using game theory. Our simulations show that incentivizing students to provide feedback requires the value obtained from receiving a feedback to exceed the cost of providing it by a large factor (greater than 7). Furthermore, hiding feedback from low-effort students incentivizes them to provide more feedback.
AU - Pandey, Vineet
AU - Chatterjee, Krishnendu
ID - 1245
IS - Februar-2016
T2 - Proceedings of the ACM Conference on Computer Supported Cooperative Work
TI - Game-theoretic models identify useful principles for peer collaboration in online learning platforms
VL - 26
ER -
TY - CONF
AB - We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural problems that arise in program analysis. We consider that each component of the concurrent system is a graph with constant treewidth, a property satisfied by the controlflow graphs of most programs. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis. The study of multiple queries allows us to consider the tradeoff between the resource usage of the one-time preprocessing and for each individual query. The traditional approach constructs the product graph of all components and applies the best-known graph algorithm on the product. In this approach, even the answer to a single query requires the transitive closure (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time. Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time, each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results showing that the worst-case running time of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (i.e., improving the worst-case bound for the shortest path problem in general graphs). Preliminary experimental results show that our algorithms perform favorably on several benchmarks.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 1437
TI - Algorithms for algebraic path properties in concurrent systems of constant treewidth components
VL - 20-22
ER -
TY - CONF
AB - We consider nondeterministic probabilistic programs with the most basic liveness property of termination. We present efficient methods for termination analysis of nondeterministic probabilistic programs with polynomial guards and assignments. Our approach is through synthesis of polynomial ranking supermartingales, that on one hand significantly generalizes linear ranking supermartingales and on the other hand is a counterpart of polynomial ranking-functions for proving termination of nonprobabilistic programs. The approach synthesizes polynomial ranking-supermartingales through Positivstellensatz's, yielding an efficient method which is not only sound, but also semi-complete over a large subclass of programs. We show experimental results to demonstrate that our approach can handle several classical programs with complex polynomial guards and assignments, and can synthesize efficient quadratic ranking-supermartingales when a linear one does not exist even for simple affine programs.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Goharshady, Amir
ID - 1386
TI - Termination analysis of probabilistic programs through Positivstellensatz's
VL - 9779
ER -
TY - CONF
AB - We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. We demonstrate our approach on an illustrative case study.
AU - Svoreňová, Mária
AU - Kretinsky, Jan
AU - Chmelik, Martin
AU - Chatterjee, Krishnendu
AU - Cěrná, Ivana
AU - Belta, Cǎlin
ID - 1689
T2 - Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control
TI - Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games
ER -
TY - CONF
AB - We consider a case study of the problem of deploying an autonomous air vehicle in a partially observable, dynamic, indoor environment from a specification given as a linear temporal logic (LTL) formula over regions of interest. We model the motion and sensing capabilities of the vehicle as a partially observable Markov decision process (POMDP). We adapt recent results for solving POMDPs with parity objectives to generate a control policy. We also extend the existing framework with a policy minimization technique to obtain a better implementable policy, while preserving its correctness. The proposed techniques are illustrated in an experimental setup involving an autonomous quadrotor performing surveillance in a dynamic environment.
AU - Svoreňová, Mária
AU - Chmelik, Martin
AU - Leahy, Kevin
AU - Eniser, Hasan
AU - Chatterjee, Krishnendu
AU - Cěrná, Ivana
AU - Belta, Cǎlin
ID - 1691
T2 - Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control
TI - Temporal logic motion planning using POMDPs with parity objectives: Case study paper
ER -
TY - JOUR
AB -
We introduce quantitative timed refinement and timed simulation (directed) metrics, incorporating zenoness checks, for timed systems. These metrics assign positive real numbers which quantify the timing mismatches between two timed systems, amongst non-zeno runs. We quantify timing mismatches in three ways: (1) the maximal timing mismatch that can arise, (2) the “steady-state” maximal timing mismatches, where initial transient timing mismatches are ignored; and (3) the (long-run) average timing mismatches amongst two systems. These three kinds of mismatches constitute three important types of timing differences. Our event times are the global times, measured from the start of the system execution, not just the time durations of individual steps. We present algorithms over timed automata for computing the three quantitative simulation distances to within any desired degree of accuracy. In order to compute the values of the quantitative simulation distances, we use a game theoretic formulation. We introduce two new kinds of objectives for two player games on finite-state game graphs: (1) eventual debit-sum level objectives, and (2) average debit-sum level objectives. We present algorithms for computing the optimal values for these objectives in graph games, and then use these algorithms to compute the values of the timed simulation distances over timed automata.
AU - Chatterjee, Krishnendu
AU - Prabhu, Vinayak
ID - 1694
IS - 9
JF - IEEE Transactions on Automatic Control
TI - Quantitative temporal simulation and refinement distances for timed systems
VL - 60
ER -
TY - JOUR
AB - In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Multi-mean-payoff and multi-energy games replace individual weights by tuples, and the limit average (resp., running sum) of each coordinate must be (resp., remain) nonnegative. We prove finite-memory determinacy of multi-energy games and show inter-reducibility of multi-mean-payoff and multi-energy games for finite-memory strategies. We improve the computational complexity for solving both classes with finite-memory strategies: we prove coNP-completeness improving the previous known EXPSPACE bound. For memoryless strategies, we show that deciding the existence of a winning strategy for the protagonist is NP-complete. We present the first solution of multi-mean-payoff games with infinite-memory strategies: we show that mean-payoff-sup objectives can be decided in NP∩coNP, whereas mean-payoff-inf objectives are coNP-complete.
AU - Velner, Yaron
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
AU - Rabinovich, Alexander
AU - Raskin, Jean
ID - 1698
IS - 4
JF - Information and Computation
TI - The complexity of multi-mean-payoff and multi-energy games
VL - 241
ER -
TY - JOUR
AB - The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.
AU - Reiter, Johannes
AU - Kanodia, Ayush
AU - Gupta, Raghav
AU - Nowak, Martin
AU - Chatterjee, Krishnendu
ID - 1709
IS - 1812
JF - Proceedings of the Royal Society of London Series B Biological Sciences
TI - Biological auctions with multiple rewards
VL - 282
ER -
TY - CONF
AB - We present a flexible framework for the automated competitive analysis of on-line scheduling algorithms for firm-deadline real-time tasks based on multi-objective graphs: Given a task set and an on-line scheduling algorithm specified as a labeled transition system, along with some optional safety, liveness, and/or limit-average constraints for the adversary, we automatically compute the competitive ratio of the algorithm w.r.t. A clairvoyant scheduler. We demonstrate the flexibility and power of our approach by comparing the competitive ratio of several on-line algorithms, including Dover, that have been proposed in the past, for various task sets. Our experimental results reveal that none of these algorithms is universally optimal, in the sense that there are task sets where other schedulers provide better performance. Our framework is hence a very useful design tool for selecting optimal algorithms for a given application.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Kößler, Alexander
AU - Schmid, Ulrich
ID - 1714
IS - January
T2 - Real-Time Systems Symposium
TI - A framework for automated competitive analysis of on-line scheduling of firm-deadline tasks
VL - 2015
ER -
TY - JOUR
AB - We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Henzinger, Thomas A
ID - 1731
IS - 12
JF - Information and Computation
TI - Randomness for free
VL - 245
ER -
TY - CONF
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 1732
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - CONF
AB - We consider partially observable Markov decision processes (POMDPs) with a set of target states and every transition is associated with an integer cost. The optimization objec- tive we study asks to minimize the expected total cost till the target set is reached, while ensuring that the target set is reached almost-surely (with probability 1). We show that for integer costs approximating the optimal cost is undecidable. For positive costs, our results are as follows: (i) we establish matching lower and upper bounds for the optimal cost and the bound is double exponential; (ii) we show that the problem of approximating the optimal cost is decidable and present ap- proximation algorithms developing on the existing algorithms for POMDPs with finite-horizon objectives. While the worst- case running time of our algorithm is double exponential, we present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 1820
T2 - Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence
TI - Optimal cost almost-sure reachability in POMDPs
VL - 5
ER -
TY - CONF
AB - Synthesis of program parts is particularly useful for concurrent systems. However, most approaches do not support common design tasks, like modifying a single process without having to re-synthesize or verify the whole system. Assume-guarantee synthesis (AGS) provides robustness against modifications of system parts, but thus far has been limited to the perfect information setting. This means that local variables cannot be hidden from other processes, which renders synthesis results cumbersome or even impossible to realize.We resolve this shortcoming by defining AGS under partial information. We analyze the complexity and decidability in different settings, showing that the problem has a high worstcase complexity and is undecidable in many interesting cases. Based on these observations, we present a pragmatic algorithm based on bounded synthesis, and demonstrate its practical applicability on several examples.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Jacobs, Swen
AU - Könighofer, Robert
ID - 1838
TI - Assume-guarantee synthesis for concurrent reactive programs with partial information
VL - 9035
ER -
TY - CONF
AB - We present MultiGain, a tool to synthesize strategies for Markov decision processes (MDPs) with multiple mean-payoff objectives. Our models are described in PRISM, and our tool uses the existing interface and simulator of PRISM. Our tool extends PRISM by adding novel algorithms for multiple mean-payoff objectives, and also provides features such as (i) generating strategies and exploring them for simulation, and checking them with respect to other properties; and (ii) generating an approximate Pareto curve for two mean-payoff objectives. In addition, we present a new practical algorithm for the analysis of MDPs with multiple mean-payoff objectives under memoryless strategies.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Forejt, Vojtěch
AU - Kučera, Antonín
ID - 1839
TI - Multigain: A controller synthesis tool for MDPs with multiple mean-payoff objectives
VL - 9035
ER -
TY - JOUR
AB - Modal transition systems (MTS) is a well-studied specification formalism of reactive systems supporting a step-wise refinement methodology. Despite its many advantages, the formalism as well as its currently known extensions are incapable of expressing some practically needed aspects in the refinement process like exclusive, conditional and persistent choices. We introduce a new model called parametric modal transition systems (PMTS) together with a general modal refinement notion that overcomes many of the limitations. We investigate the computational complexity of modal and thorough refinement checking on PMTS and its subclasses and provide a direct encoding of the modal refinement problem into quantified Boolean formulae, allowing us to employ state-of-the-art QBF solvers for modal refinement checking. The experiments we report on show that the feasibility of refinement checking is more influenced by the degree of nondeterminism rather than by the syntactic restrictions on the types of formulae allowed in the description of the PMTS.
AU - Beneš, Nikola
AU - Kretinsky, Jan
AU - Larsen, Kim
AU - Möller, Mikael
AU - Sickert, Salomon
AU - Srba, Jiří
ID - 1846
IS - 2-3
JF - Acta Informatica
TI - Refinement checking on parametric modal transition systems
VL - 52
ER -
TY - JOUR
AB - We consider mating strategies for females who search for males sequentially during a season of limited length. We show that the best strategy rejects a given male type if encountered before a time-threshold but accepts him after. For frequency-independent benefits, we obtain the optimal time-thresholds explicitly for both discrete and continuous distributions of males, and allow for mistakes being made in assessing the correct male type. When the benefits are indirect (genes for the offspring) and the population is under frequency-dependent ecological selection, the benefits depend on the mating strategy of other females as well. This case is particularly relevant to speciation models that seek to explore the stability of reproductive isolation by assortative mating under frequency-dependent ecological selection. We show that the indirect benefits are to be quantified by the reproductive values of couples, and describe how the evolutionarily stable time-thresholds can be found. We conclude with an example based on the Levene model, in which we analyze the evolutionarily stable assortative mating strategies and the strength of reproductive isolation provided by them.
AU - Priklopil, Tadeas
AU - Kisdi, Eva
AU - Gyllenberg, Mats
ID - 1851
IS - 4
JF - Evolution
TI - Evolutionarily stable mating decisions for sequentially searching females and the stability of reproductive isolation by assortative mating
VL - 69
ER -
TY - JOUR
AB - The traditional synthesis question given a specification asks for the automatic construction of a system that satisfies the specification, whereas often there exists a preference order among the different systems that satisfy the given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimal synthesis problem: given an omega-regular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification under the input assumption, synthesize a system that optimizes the measured value. For safety specifications and quantitative measures that are defined by mean-payoff automata, the optimal synthesis problem reduces to finding a strategy in a Markov decision process (MDP) that is optimal for a long-run average reward objective, which can be achieved in polynomial time. For general omega-regular specifications along with mean-payoff automata, the solution rests on a new, polynomial-time algorithm for computing optimal strategies in MDPs with mean-payoff parity objectives. Our algorithm constructs optimal strategies that consist of two memoryless strategies and a counter. The counter is in general not bounded. To obtain a finite-state system, we show how to construct an ε-optimal strategy with a bounded counter, for all ε > 0. Furthermore, we show how to decide in polynomial time if it is possible to construct an optimal finite-state system (i.e., a system without a counter) for a given specification. We have implemented our approach and the underlying algorithms in a tool that takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. We present some experimental results showing optimal systems that were automatically generated in this way.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
AU - Singh, Rohit
ID - 1856
IS - 1
JF - Journal of the ACM
TI - Measuring and synthesizing systems in probabilistic environments
VL - 62
ER -
TY - JOUR
AB - We consider partially observable Markov decision processes (POMDPs) with limit-average payoff, where a reward value in the interval [0,1] is associated with every transition, and the payoff of an infinite path is the long-run average of the rewards. We consider two types of path constraints: (i) a quantitative constraint defines the set of paths where the payoff is at least a given threshold λ1ε(0,1]; and (ii) a qualitative constraint which is a special case of the quantitative constraint with λ1=1. We consider the computation of the almost-sure winning set, where the controller needs to ensure that the path constraint is satisfied with probability 1. Our main results for qualitative path constraints are as follows: (i) the problem of deciding the existence of a finite-memory controller is EXPTIME-complete; and (ii) the problem of deciding the existence of an infinite-memory controller is undecidable. For quantitative path constraints we show that the problem of deciding the existence of a finite-memory controller is undecidable. We also present a prototype implementation of our EXPTIME algorithm and experimental results on several examples.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
ID - 1873
JF - Artificial Intelligence
TI - POMDPs under probabilistic semantics
VL - 221
ER -
TY - CONF
AB - We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations.
AU - Fahrenberg, Uli
AU - Kretinsky, Jan
AU - Legay, Axel
AU - Traonouez, Louis
ID - 1882
TI - Compositionality for quantitative specifications
VL - 8997
ER -
TY - JOUR
AB - Opacity is a generic security property, that has been defined on (non-probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an external observer, the value of interest for opacity is a measure of the set of runs disclosing the secret. We extend this definition to the richer framework of Markov decision processes, where non-deterministicchoice is combined with probabilistic transitions, and we study related decidability problems with partial or complete observation hypotheses for the schedulers. We prove that all questions are decidable with complete observation and ω-regular secrets. With partial observation, we prove that all quantitative questions are undecidable but the question whether a system is almost surely non-opaquebecomes decidable for a restricted class of ω-regular secrets, as well as for all ω-regular secrets under finite-memory schedulers.
AU - Bérard, Béatrice
AU - Chatterjee, Krishnendu
AU - Sznajder, Nathalie
ID - 2034
IS - 1
JF - Information Processing Letters
TI - Probabilistic opacity for Markov decision processes
VL - 115
ER -
TY - JOUR
AB - We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-payoff games that are known to be coNP-complete, multi-dimensional total-payoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Randour, Mickael
AU - Raskin, Jean
ID - 523
IS - 6
JF - Information and Computation
TI - Looking at mean-payoff and total-payoff through windows
VL - 242
ER -
TY - JOUR
AB - We consider concurrent games played by two players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study the most fundamental objective for concurrent games, namely, mean-payoff or limit-average objective, where a reward is associated to each transition, and the goal of player 1 is to maximize the long-run average of the rewards, and the objective of player 2 is strictly the opposite (i.e., the games are zero-sum). The path constraint for player 1 could be qualitative, i.e., the mean-payoff is the maximal reward, or arbitrarily close to it; or quantitative, i.e., a given threshold between the minimal and maximal reward. We consider the computation of the almost-sure (resp. positive) winning sets, where player 1 can ensure that the path constraint is satisfied with probability 1 (resp. positive probability). Almost-sure winning with qualitative constraint exactly corresponds to the question of whether there exists a strategy to ensure that the payoff is the maximal reward of the game. Our main results for qualitative path constraints are as follows: (1) we establish qualitative determinacy results that show that for every state either player 1 has a strategy to ensure almost-sure (resp. positive) winning against all player-2 strategies, or player 2 has a spoiling strategy to falsify almost-sure (resp. positive) winning against all player-1 strategies; (2) we present optimal strategy complexity results that precisely characterize the classes of strategies required for almost-sure and positive winning for both players; and (3) we present quadratic time algorithms to compute the almost-sure and the positive winning sets, matching the best known bound of the algorithms for much simpler problems (such as reachability objectives). For quantitative constraints we show that a polynomial time solution for the almost-sure or the positive winning set would imply a solution to a long-standing open problem (of solving the value problem of turn-based deterministic mean-payoff games) that is not known to be solvable in polynomial time.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 524
IS - 6
JF - Information and Computation
TI - Qualitative analysis of concurrent mean payoff games
VL - 242
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics.
Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions.
Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Komarkova, Zuzana
AU - Kretinsky, Jan
ID - 5429
SN - 2664-1690
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - GEN
AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean- payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m = O ( n ) ) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a mul- tiplicative factor of ∊ in time O ( n · log( n/∊ )) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O ( n · log( | a · b · n | )) = O ( n · log( n · W )) , when the output is a b , as compared to the previously best known algorithm with running time O ( n 2 · log( n · W )) . Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O ( n 2 · m ) time and the associated decision problem can be solved in O ( n · m ) time, improving the previous known O ( n 3 · m · log( n · W )) and O ( n 2 · m ) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O ( n · log n ) time, improving the previous known O ( n 4 · log( n · W )) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5430
SN - 2664-1690
TI - Faster algorithms for quantitative verification in constant treewidth graphs
ER -
TY - GEN
AB - We consider finite-state concurrent stochastic games, played by k>=2 players for an infinite number of rounds, where in every round, each player simultaneously and independently of the other players chooses an action, whereafter the successor state is determined by a probability distribution given by the current state and the chosen actions. We consider reachability objectives that given a target set of states require that some state in the target set is visited, and the dual safety objectives that given a target set require that only states in the target set are visited. We are interested in the complexity of stationary strategies measured by their patience, which is defined as the inverse of the smallest non-zero probability employed.
Our main results are as follows: We show that in two-player zero-sum concurrent stochastic games (with reachability objective for one player and the complementary safety objective for the other player): (i) the optimal bound on the patience of optimal and epsilon-optimal strategies, for both players is doubly exponential; and (ii) even in games with a single non-absorbing state exponential (in the number of actions) patience is necessary. In general we study the class of non-zero-sum games admitting epsilon-Nash equilibria. We show that if there is at least one player with reachability objective, then doubly-exponential patience is needed in general for epsilon-Nash equilibrium strategies, whereas in contrast if all players have safety objectives, then the optimal bound on patience for epsilon-Nash equilibrium strategies is only exponential.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Hansen, Kristoffer
ID - 5431
SN - 2664-1690
TI - The patience of concurrent stochastic games with safety and reachability objectives
ER -
TY - GEN
AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom in the context of evolution.The replacement graph specifies who competes with whom for reproduction.
The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability.
Our main results are:
(1) We show that the qualitative question is NP-complete and the quantitative approximation question is #P-hard in the special case when the interaction and the replacement graphs coincide and even with the restriction that the resident individuals do not reproduce (which corresponds to an invading population taking over an empty structure).
(2) We show that in general the qualitative question is PSPACE-complete and the quantitative approximation question is PSPACE-hard and can be solved in exponential time.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Nowak, Martin
ID - 5432
SN - 2664-1690
TI - The complexity of evolutionary games on graphs
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives.
There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector.
We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee).
Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP.
We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Komarkova, Zuzana
AU - Kretinsky, Jan
ID - 5435
SN - 2664-1690
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - GEN
AB - Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata, nor in any other know decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata which makes it possible to express important quantitative properties such as average response time.
In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in run-time verification. We establish an almost complete decidability picture for the basic decision problems about nested weighted automata, and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 5436
SN - 2664-1690
TI - Nested weighted automata
ER -
TY - GEN
AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property.
The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let $n$ denote the number of nodes of a graph, $m$ the number of edges (for constant treewidth graphs $m=O(n)$) and $W$ the largest absolute value of the weights.
Our main theoretical results are as follows.
First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of $\epsilon$ in time $O(n \cdot \log (n/\epsilon))$ and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time $O(n \cdot \log (|a\cdot b|))=O(n\cdot\log (n\cdot W))$, when the output is $\frac{a}{b}$, as compared to the previously best known algorithm with running time $O(n^2 \cdot \log (n\cdot W))$. Third, for the minimum initial credit problem we show that (i)~for general graphs the problem can be solved in $O(n^2\cdot m)$ time and the associated decision problem can be solved in $O(n\cdot m)$ time, improving the previous known $O(n^3\cdot m\cdot \log (n\cdot W))$ and $O(n^2 \cdot m)$ bounds, respectively; and (ii)~for constant treewidth graphs we present an algorithm that requires $O(n\cdot \log n)$ time, improving the previous known $O(n^4 \cdot \log (n \cdot W))$ bound.
We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5437
SN - 2664-1690
TI - Faster algorithms for quantitative verification in constant treewidth graphs
ER -
TY - GEN
AB - The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1, L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses.
The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Ibsen-Jensen, Rasmus
AU - Otop, Jan
ID - 5438
SN - 2664-1690
TI - Edit distance for pushdown automata
ER -
TY - GEN
AB - Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom for payoff in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. The fitness (or the reproductive rate) is a non-negative number, and depends on the payoff. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are as follows: First, we consider a special case of the general problem, where the residents do not reproduce. We show that the qualitative question is NP-complete, and the quantitative approximation question is #P-complete, and the hardness results hold even in the special case where the interaction and the replacement graphs coincide. Second, we show that in general both the qualitative and the quantitative approximation questions are PSPACE-complete. The PSPACE-hardness result for quantitative approximation holds even when the fitness is always positive.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Nowak, Martin
ID - 5440
SN - 2664-1690
TI - The complexity of evolutionary games on graphs
ER -
TY - GEN
AB - We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural problems that arise in program analysis. We consider that each component of the concurrent system is a graph with constant treewidth, a property satisfied by the controlflow graphs of most programs. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis. The study of multiple queries allows us to consider the tradeoff between the resource usage of the one-time preprocessing and for each individual query. The traditional approach constructs the product graph of all components and applies the best-known graph algorithm on the product. In this approach, even the answer to a single query requires the transitive closure (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time. Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time, each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results showing that the worst-case running time of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (i.e., improving the worst-case bound for the shortest path problem in general graphs). Preliminary experimental results show that our algorithms perform favorably on several benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Goharshady, Amir
AU - Pavlogiannis, Andreas
ID - 5441
SN - 2664-1690
TI - Algorithms for algebraic path properties in concurrent systems of constant treewidth components
ER -
TY - GEN
AB - POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Davies, Jessica
ID - 5443
SN - 2664-1690
TI - A symbolic SAT-based algorithm for almost-sure reachability with small strategies in POMDPs
ER -
TY - GEN
AB - A comprehensive understanding of the clonal evolution of cancer is critical for understanding neoplasia. Genome-wide sequencing data enables evolutionary studies at unprecedented depth. However, classical phylogenetic methods often struggle with noisy sequencing data of impure DNA samples and fail to detect subclones that have different evolutionary trajectories. We have developed a tool, called Treeomics, that allows us to reconstruct the phylogeny of a cancer with commonly available sequencing technologies. Using Bayesian inference and Integer Linear Programming, robust phylogenies consistent with the biological processes underlying cancer evolution were obtained for pancreatic, ovarian, and prostate cancers. Furthermore, Treeomics correctly identified sequencing artifacts such as those resulting from low statistical power; nearly 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumor heterogeneity among distinct samples. Importantly, we show that the evolutionary trees generated with Treeomics are mathematically optimal.
AU - Reiter, Johannes
AU - Makohon-Moore, Alvin
AU - Gerold, Jeffrey
AU - Bozic, Ivana
AU - Chatterjee, Krishnendu
AU - Iacobuzio-Donahue, Christine
AU - Vogelstein, Bert
AU - Nowak, Martin
ID - 5444
SN - 2664-1690
TI - Reconstructing robust phylogenies of metastatic cancers
ER -
TY - DATA
AB - This repository contains the experimental part of the CAV 2015 publication Counterexample Explanation by Learning Small Strategies in Markov Decision Processes.
We extended the probabilistic model checker PRISM to represent strategies of Markov Decision Processes as Decision Trees.
The archive contains a java executable version of the extended tool (prism_dectree.jar) together with a few examples of the PRISM benchmark library.
To execute the program, please have a look at the README.txt, which provides instructions and further information on the archive.
The archive contains scripts that (if run often enough) reproduces the data presented in the publication.
AU - Fellner, Andreas
ID - 5549
KW - Markov Decision Process
KW - Decision Tree
KW - Probabilistic Verification
KW - Counterexample Explanation
TI - Experimental part of CAV 2015 publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes
ER -
TY - THES
AB - Cancer results from an uncontrolled growth of abnormal cells. Sequentially accumulated genetic and epigenetic alterations decrease cell death and increase cell replication. We used mathematical models to quantify the effect of driver gene mutations. The recently developed targeted therapies can lead to dramatic regressions. However, in solid cancers, clinical responses are often short-lived because resistant cancer cells evolve. We estimated that approximately 50 different mutations can confer resistance to a typical targeted therapeutic agent. We find that resistant cells are likely to be present in expanded subclones before the start of the treatment. The dominant strategy to prevent the evolution of resistance is combination therapy. Our analytical results suggest that in most patients, dual therapy, but not monotherapy, can result in long-term disease control. However, long-term control can only occur if there are no possible mutations in the genome that can cause cross-resistance to both drugs. Furthermore, we showed that simultaneous therapy with two drugs is much more likely to result in long-term disease control than sequential therapy with the same drugs. To improve our understanding of the underlying subclonal evolution we reconstruct the evolutionary history of a patient's cancer from next-generation sequencing data of spatially-distinct DNA samples. Using a quantitative measure of genetic relatedness, we found that pancreatic cancers and their metastases demonstrated a higher level of relatedness than that expected for any two cells randomly taken from a normal tissue. This minimal amount of genetic divergence among advanced lesions indicates that genetic heterogeneity, when quantitatively defined, is not a fundamental feature of the natural history of untreated pancreatic cancers. Our newly developed, phylogenomic tool Treeomics finds evidence for seeding patterns of metastases and can directly be used to discover rules governing the evolution of solid malignancies to transform cancer into a more predictable disease.
AU - Reiter, Johannes
ID - 1400
TI - The subclonal evolution of cancer
ER -
TY - CONF
AB - Simple board games, like Tic-Tac-Toe and CONNECT-4, play an important role not only in the development of mathematical and logical skills, but also in the emotional and social development. In this paper, we address the problem of generating targeted starting positions for such games. This can facilitate new approaches for bringing novice players to mastery, and also leads to discovery of interesting game variants. We present an approach that generates starting states of varying hardness levels for player 1 in a two-player board game, given rules of the board game, the desired number of steps required for player 1 to win, and the expertise levels of the two players. Our approach leverages symbolic methods and iterative simulation to efficiently search the extremely large state space. We present experimental results that include discovery of states of varying hardness levels for several simple grid-based board games. The presence of such states for standard game variants like 4×4 Tic-Tac-Toe opens up new games to be played that have never been played as the default start state is heavily biased.
AU - Ahmed, Umair
AU - Chatterjee, Krishnendu
AU - Gulwani, Sumit
ID - 1481
T2 - Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence
TI - Automatic generation of alternative starting positions for simple traditional board games
VL - 2
ER -
TY - CONF
AB - We consider weighted automata with both positive and negative integer weights on edges and
study the problem of synchronization using adaptive strategies that may only observe whether
the current weight-level is negative or nonnegative. We show that the synchronization problem is decidable in polynomial time for deterministic weighted automata.
AU - Kretinsky, Jan
AU - Larsen, Kim
AU - Laursen, Simon
AU - Srba, Jiří
ID - 1499
TI - Polynomial time decidability of weighted synchronization under partial observability
VL - 42
ER -
TY - JOUR
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability. We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph algorithms with quadratic complexity to compute the simulation relation. We present an automated technique for assume-guarantee style reasoning for compositional analysis of two-player games by giving a counterexample guided abstraction-refinement approach to compute our new simulation relation. We show a tight link between two-player games and MDPs, and as a consequence the results for games are lifted to MDPs with qualitative properties. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Daca, Przemyslaw
ID - 1501
IS - 2
JF - Formal Methods in System Design
TI - CEGAR for compositional analysis of qualitative properties in Markov decision processes
VL - 47
ER -
TY - CONF
AB - We extend the theory of input-output conformance with operators for merge and quotient. The former is useful when testing against multiple requirements or views. The latter can be used to generate tests for patches of an already tested system. Both operators can combine systems with different action alphabets, which is usually the case when constructing complex systems and specifications from parts, for instance different views as well as newly defined functionality of a~previous version of the system.
AU - Beneš, Nikola
AU - Daca, Przemyslaw
AU - Henzinger, Thomas A
AU - Kretinsky, Jan
AU - Nickovic, Dejan
ID - 1502
SN - 978-1-4503-3471-6
TI - Complete composition operators for IOCO-testing theory
ER -
TY - JOUR
AB - There are deep, yet largely unexplored, connections between computer science and biology. Both disciplines examine how information proliferates in time and space. Central results in computer science describe the complexity of algorithms that solve certain classes of problems. An algorithm is deemed efficient if it can solve a problem in polynomial time, which means the running time of the algorithm is a polynomial function of the length of the input. There are classes of harder problems for which the fastest possible algorithm requires exponential time. Another criterion is the space requirement of the algorithm. There is a crucial distinction between algorithms that can find a solution, verify a solution, or list several distinct solutions in given time and space. The complexity hierarchy that is generated in this way is the foundation of theoretical computer science. Precise complexity results can be notoriously difficult. The famous question whether polynomial time equals nondeterministic polynomial time (i.e., P = NP) is one of the hardest open problems in computer science and all of mathematics. Here, we consider simple processes of ecological and evolutionary spatial dynamics. The basic question is: What is the probability that a new invader (or a new mutant)will take over a resident population?We derive precise complexity results for a variety of scenarios. We therefore show that some fundamental questions in this area cannot be answered by simple equations (assuming that P is not equal to NP).
AU - Ibsen-Jensen, Rasmus
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 1559
IS - 51
JF - PNAS
TI - Computational complexity of ecological and evolutionary spatial dynamics
VL - 112
ER -
TY - CONF
AB - Quantitative extensions of temporal logics have recently attracted significant attention. In this work, we study frequency LTL (fLTL), an extension of LTL which allows to speak about frequencies of events along an execution. Such an extension is particularly useful for probabilistic systems that often cannot fulfil strict qualitative guarantees on the behaviour. It has been recently shown that controller synthesis for Markov decision processes and fLTL is decidable when all the bounds on frequencies are 1. As a step towards a complete quantitative solution, we show that the problem is decidable for the fragment fLTL\GU, where U does not occur in the scope of G (but still F can). Our solution is based on a novel translation of such quantitative formulae into equivalent deterministic automata.
AU - Forejt, Vojtěch
AU - Krčál, Jan
AU - Kretinsky, Jan
ID - 1594
TI - Controller synthesis for MDPs and frequency LTL\GU
VL - 9450
ER -
TY - JOUR
AB - We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives, and examine the problem of computing the set of almost-sure winning vertices such that the objective can be ensured with probability 1 from these vertices. We study for the first time the average-case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average-case running time is linear (as compared to the worst-case linear number of iterations and quadratic time complexity). Second, for the average-case analysis over all MDPs we show that the expected number of iterations is constant and the average-case running time is linear (again as compared to the worst-case linear number of iterations and quadratic time complexity). Finally we also show that when all MDPs are equally likely, the probability that the classical algorithm requires more than a constant number of iterations is exponentially small.
AU - Chatterjee, Krishnendu
AU - Joglekar, Manas
AU - Shah, Nisarg
ID - 1598
IS - 3
JF - Theoretical Computer Science
TI - Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives
VL - 573
ER -
TY - CONF
AB - We propose a flexible exchange format for ω-automata, as typically used in formal verification, and implement support for it in a range of established tools. Our aim is to simplify the interaction of tools, helping the research community to build upon other people’s work. A key feature of the format is the use of very generic acceptance conditions, specified by Boolean combinations of acceptance primitives, rather than being limited to common cases such as Büchi, Streett, or Rabin. Such flexibility in the choice of acceptance conditions can be exploited in applications, for example in probabilistic model checking, and furthermore encourages the development of acceptance-agnostic tools for automata manipulations. The format allows acceptance conditions that are either state-based or transition-based, and also supports alternating automata.
AU - Babiak, Tomáš
AU - Blahoudek, František
AU - Duret Lutz, Alexandre
AU - Klein, Joachim
AU - Kretinsky, Jan
AU - Mueller, Daniel
AU - Parker, David
AU - Strejček, Jan
ID - 1601
TI - The Hanoi omega-automata format
VL - 9206
ER -
TY - JOUR
AB - Interprocedural analysis is at the heart of numerous applications in programming languages, such as alias analysis, constant propagation, etc. Recursive state machines (RSMs) are standard models for interprocedural analysis. We consider a general framework with RSMs where the transitions are labeled from a semiring, and path properties are algebraic with semiring operations. RSMs with algebraic path properties can model interprocedural dataflow analysis problems, the shortest path problem, the most probable path problem, etc. The traditional algorithms for interprocedural analysis focus on path properties where the starting point is fixed as the entry point of a specific method. In this work, we consider possible multiple queries as required in many applications such as in alias analysis. The study of multiple queries allows us to bring in a very important algorithmic distinction between the resource usage of the one-time preprocessing vs for each individual query. The second aspect that we consider is that the control flow graphs for most programs have constant treewidth. Our main contributions are simple and implementable algorithms that supportmultiple queries for algebraic path properties for RSMs that have constant treewidth. Our theoretical results show that our algorithms have small additional one-time preprocessing, but can answer subsequent queries significantly faster as compared to the current best-known solutions for several important problems, such as interprocedural reachability and shortest path. We provide a prototype implementation for interprocedural reachability and intraprocedural shortest path that gives a significant speed-up on several benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
AU - Goyal, Prateesh
ID - 1602
IS - 1
JF - ACM SIGPLAN Notices
TI - Faster algorithms for algebraic path properties in recursive state machines with constant treewidth
VL - 50
ER -
TY - CONF
AB - For deterministic systems, a counterexample to a property can simply be an error trace, whereas counterexamples in probabilistic systems are necessarily more complex. For instance, a set of erroneous traces with a sufficient cumulative probability mass can be used. Since these are too large objects to understand and manipulate, compact representations such as subchains have been considered. In the case of probabilistic systems with non-determinism, the situation is even more complex. While a subchain for a given strategy (or scheduler, resolving non-determinism) is a straightforward choice, we take a different approach. Instead, we focus on the strategy itself, and extract the most important decisions it makes, and present its succinct representation.
The key tools we employ to achieve this are (1) introducing a concept of importance of a state w.r.t. the strategy, and (2) learning using decision trees. There are three main consequent advantages of our approach. Firstly, it exploits the quantitative information on states, stressing the more important decisions. Secondly, it leads to a greater variability and degree of freedom in representing the strategies. Thirdly, the representation uses a self-explanatory data structure. In summary, our approach produces more succinct and more explainable strategies, as opposed to e.g. binary decision diagrams. Finally, our experimental results show that we can extract several rules describing the strategy even for very large systems that do not fit in memory, and based on the rules explain the erroneous behaviour.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Fellner, Andreas
AU - Kretinsky, Jan
ID - 1603
TI - Counterexample explanation by learning small strategies in Markov decision processes
VL - 9206
ER -
TY - JOUR
AB - We consider the quantitative analysis problem for interprocedural control-flow graphs (ICFGs). The input consists of an ICFG, a positive weight function that assigns every transition a positive integer-valued number, and a labelling of the transitions (events) as good, bad, and neutral events. The weight function assigns to each transition a numerical value that represents ameasure of how good or bad an event is. The quantitative analysis problem asks whether there is a run of the ICFG where the ratio of the sum of the numerical weights of good events versus the sum of weights of bad events in the long-run is at least a given threshold (or equivalently, to compute the maximal ratio among all valid paths in the ICFG). The quantitative analysis problem for ICFGs can be solved in polynomial time, and we present an efficient and practical algorithm for the problem. We show that several problems relevant for static program analysis, such as estimating the worst-case execution time of a program or the average energy consumption of a mobile application, can be modeled in our framework. We have implemented our algorithm as a tool in the Java Soot framework. We demonstrate the effectiveness of our approach with two case studies. First, we show that our framework provides a sound approach (no false positives) for the analysis of inefficiently-used containers. Second, we show that our approach can also be used for static profiling of programs which reasons about methods that are frequently invoked. Our experimental results show that our tool scales to relatively large benchmarks, and discovers relevant and useful information that can be used to optimize performance of the programs.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Velner, Yaron
ID - 1604
IS - 1
JF - Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT
SN - 978-1-4503-3300-9
TI - Quantitative interprocedural analysis
VL - 50
ER -
TY - CONF
AB - The synthesis problem asks for the automatic construction of a system from its specification. In the traditional setting, the system is “constructed from scratch” rather than composed from reusable components. However, this is rare in practice, and almost every non-trivial software system relies heavily on the use of libraries of reusable components. Recently, Lustig and Vardi introduced dataflow and controlflow synthesis from libraries of reusable components. They proved that dataflow synthesis is undecidable, while controlflow synthesis is decidable. The problem of controlflow synthesis from libraries of probabilistic components was considered by Nain, Lustig and Vardi, and was shown to be decidable for qualitative analysis (that asks that the specification be satisfied with probability 1). Our main contribution for controlflow synthesis from probabilistic components is to establish better complexity bounds for the qualitative analysis problem, and to show that the more general quantitative problem is undecidable. For the qualitative analysis, we show that the problem (i) is EXPTIME-complete when the specification is given as a deterministic parity word automaton, improving the previously known 2EXPTIME upper bound; and (ii) belongs to UP ∩ coUP and is parity-games hard, when the specification is given directly as a parity condition on the components, improving the previously known EXPTIME upper bound.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Vardi, Moshe
ID - 1609
TI - The complexity of synthesis from probabilistic components
VL - 9135
ER -
TY - CONF
AB - The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1,L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to pushdown automata is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Ibsen-Jensen, Rasmus
AU - Otop, Jan
ID - 1610
IS - Part II
TI - Edit distance for pushdown automata
VL - 9135
ER -
TY - JOUR
AB - Population structure can facilitate evolution of cooperation. In a structured population, cooperators can form clusters which resist exploitation by defectors. Recently, it was observed that a shift update rule is an extremely strong amplifier of cooperation in a one dimensional spatial model. For the shift update rule, an individual is chosen for reproduction proportional to fecundity; the offspring is placed next to the parent; a random individual dies. Subsequently, the population is rearranged (shifted) until all individual cells are again evenly spaced out. For large population size and a one dimensional population structure, the shift update rule favors cooperation for any benefit-to-cost ratio greater than one. But every attempt to generalize shift updating to higher dimensions while maintaining its strong effect has failed. The reason is that in two dimensions the clusters are fragmented by the movements caused by rearranging the cells. Here we introduce the natural phenomenon of a repulsive force between cells of different types. After a birth and death event, the cells are being rearranged minimizing the overall energy expenditure. If the repulsive force is sufficiently high, shift becomes a strong promoter of cooperation in two dimensions.
AU - Pavlogiannis, Andreas
AU - Chatterjee, Krishnendu
AU - Adlam, Ben
AU - Nowak, Martin
ID - 1624
JF - Scientific Reports
TI - Cellular cooperation with shift updating and repulsion
VL - 5
ER -
TY - CONF
AB - Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata, nor in any other know decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata which makes it possible to express important quantitative properties such as average response time. In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in run-time verification. We establish an almost complete decidability picture for the basic decision problems about nested weighted automata, and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 1656
T2 - Proceedings - Symposium on Logic in Computer Science
TI - Nested weighted automata
VL - 2015-July
ER -
TY - CONF
AB - We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) ~the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) ~the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector. We consider optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., Ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems, which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.
AU - Chatterjee, Krishnendu
AU - Komárková, Zuzana
AU - Kretinsky, Jan
ID - 1657
TI - Unifying two views on multiple mean-payoff objectives in Markov decision processes
ER -
TY - CONF
AB - We study the pattern frequency vector for runs in probabilistic Vector Addition Systems with States (pVASS). Intuitively, each configuration of a given pVASS is assigned one of finitely many patterns, and every run can thus be seen as an infinite sequence of these patterns. The pattern frequency vector assigns to each run the limit of pattern frequencies computed for longer and longer prefixes of the run. If the limit does not exist, then the vector is undefined. We show that for one-counter pVASS, the pattern frequency vector is defined and takes one of finitely many values for almost all runs. Further, these values and their associated probabilities can be approximated up to an arbitrarily small relative error in polynomial time. For stable two-counter pVASS, we show the same result, but we do not provide any upper complexity bound. As a byproduct of our study, we discover counterexamples falsifying some classical results about stochastic Petri nets published in the 80s.
AU - Brázdil, Tomáš
AU - Kiefer, Stefan
AU - Kučera, Antonín
AU - Novotny, Petr
ID - 1660
TI - Long-run average behaviour of probabilistic vector addition systems
ER -
TY - CONF
AB - The computation of the winning set for one-pair Streett objectives and for k-pair Streett objectives in (standard) graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formed ness of specifications, and the synthesis of reactive systems. We give faster algorithms for the computation of the winning set for (1) one-pair Streett objectives (aka parity-3 problem) in game graphs and (2) for k-pair Streett objectives in graphs. For both problems this represents the first improvement in asymptotic running time in 15 years.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Loitzenbauer, Veronika
ID - 1661
T2 - Proceedings - Symposium on Logic in Computer Science
TI - Improved algorithms for one-pair and k-pair Streett objectives
VL - 2015-July
ER -
TY - JOUR
AB - Which genetic alterations drive tumorigenesis and how they evolve over the course of disease and therapy are central questions in cancer biology. Here we identify 44 recurrently mutated genes and 11 recurrent somatic copy number variations through whole-exome sequencing of 538 chronic lymphocytic leukaemia (CLL) and matched germline DNA samples, 278 of which were collected in a prospective clinical trial. These include previously unrecognized putative cancer drivers (RPS15, IKZF3), and collectively identify RNA processing and export, MYC activity, and MAPK signalling as central pathways involved in CLL. Clonality analysis of this large data set further enabled reconstruction of temporal relationships between driver events. Direct comparison between matched pre-treatment and relapse samples from 59 patients demonstrated highly frequent clonal evolution. Thus, large sequencing data sets of clinically informative samples enable the discovery of novel genes associated with cancer, the network of relationships between the driver events, and their impact on disease relapse and clinical outcome.
AU - Landau, Dan
AU - Tausch, Eugen
AU - Taylor Weiner, Amaro
AU - Stewart, Chip
AU - Reiter, Johannes
AU - Bahlo, Jasmin
AU - Kluth, Sandra
AU - Božić, Ivana
AU - Lawrence, Michael
AU - Böttcher, Sebastian
AU - Carter, Scott
AU - Cibulskis, Kristian
AU - Mertens, Daniel
AU - Sougnez, Carrie
AU - Rosenberg, Mara
AU - Hess, Julian
AU - Edelmann, Jennifer
AU - Kless, Sabrina
AU - Kneba, Michael
AU - Ritgen, Matthias
AU - Fink, Anna
AU - Fischer, Kirsten
AU - Gabriel, Stacey
AU - Lander, Eric
AU - Nowak, Martin
AU - Döhner, Hartmut
AU - Hallek, Michael
AU - Neuberg, Donna
AU - Getz, Gad
AU - Stilgenbauer, Stephan
AU - Wu, Catherine
ID - 1665
IS - 7574
JF - Nature
TI - Mutations driving CLL and their evolution in progression and relapse
VL - 526
ER -
TY - CONF
AB - We consider parametric version of fixed-delay continuoustime Markov chains (or equivalently deterministic and stochastic Petri nets, DSPN) where fixed-delay transitions are specified by parameters, rather than concrete values. Our goal is to synthesize values of these parameters that, for a given cost function, minimise expected total cost incurred before reaching a given set of target states. We show that under mild assumptions, optimal values of parameters can be effectively approximated using translation to a Markov decision process (MDP) whose actions correspond to discretized values of these parameters. To this end we identify and overcome several interesting phenomena arising in systems with fixed delays.
AU - Brázdil, Tomáš
AU - Korenčiak, L'Uboš
AU - Krčál, Jan
AU - Novotny, Petr
AU - Řehák, Vojtěch
ID - 1667
TI - Optimizing performance of continuous-time stochastic systems using timeout synthesis
VL - 9259
ER -
TY - JOUR
AB - When a new mutant arises in a population, there is a probability it outcompetes the residents and fixes. The structure of the population can affect this fixation probability. Suppressing population structures reduce the difference between two competing variants, while amplifying population structures enhance the difference. Suppressors are ubiquitous and easy to construct, but amplifiers for the large population limit are more elusive and only a few examples have been discovered. Whether or not a population structure is an amplifier of selection depends on the probability distribution for the placement of the invading mutant. First, we prove that there exist only bounded amplifiers for adversarial placement-that is, for arbitrary initial conditions. Next, we show that the Star population structure, which is known to amplify for mutants placed uniformly at random, does not amplify for mutants that arise through reproduction and are therefore placed proportional to the temperatures of the vertices. Finally, we construct population structures that amplify for all mutational events that arise through reproduction, uniformly at random, or through some combination of the two.
AU - Adlam, Ben
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 1673
IS - 2181
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
TI - Amplifiers of selection
VL - 471
ER -
TY - JOUR
AB - In many social situations, individuals endeavor to find the single best possible partner, but are constrained to evaluate the candidates in sequence. Examples include the search for mates, economic partnerships, or any other long-term ties where the choice to interact involves two parties. Surprisingly, however, previous theoretical work on mutual choice problems focuses on finding equilibrium solutions, while ignoring the evolutionary dynamics of decisions. Empirically, this may be of high importance, as some equilibrium solutions can never be reached unless the population undergoes radical changes and a sufficient number of individuals change their decisions simultaneously. To address this question, we apply a mutual choice sequential search problem in an evolutionary game-theoretical model that allows one to find solutions that are favored by evolution. As an example, we study the influence of sequential search on the evolutionary dynamics of cooperation. For this, we focus on the classic snowdrift game and the prisoner’s dilemma game.
AU - Priklopil, Tadeas
AU - Chatterjee, Krishnendu
ID - 1681
IS - 4
JF - Games
TI - Evolution of decisions in population games with sequentially searching individuals
VL - 6
ER -
TY - CONF
AB - We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property. The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let n denote the number of nodes of a graph, m the number of edges (for constant treewidth graphs m=O(n)) and W the largest absolute value of the weights. Our main theoretical results are as follows. First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of ϵ in time O(n⋅log(n/ϵ)) and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time O(n⋅log(|a⋅b|))=O(n⋅log(n⋅W)), when the output is ab, as compared to the previously best known algorithm with running time O(n2⋅log(n⋅W)). Third, for the minimum initial credit problem we show that (i) for general graphs the problem can be solved in O(n2⋅m) time and the associated decision problem can be solved in O(n⋅m) time, improving the previous known O(n3⋅m⋅log(n⋅W)) and O(n2⋅m) bounds, respectively; and (ii) for constant treewidth graphs we present an algorithm that requires O(n⋅logn) time, improving the previous known O(n4⋅log(n⋅W)) bound. We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 1607
TI - Faster algorithms for quantitative verification in constant treewidth graphs
VL - 9206
ER -
TY - JOUR
AB - Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express ω ω -regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on vector addition systems with states. Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts.
AU - Chatterjee, Krishnendu
AU - Randour, Mickael
AU - Raskin, Jean
ID - 2716
IS - 3-4
JF - Acta Informatica
TI - Strategy synthesis for multi-dimensional quantitative objectives
VL - 51
ER -
TY - JOUR
AB - The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces, and how to synthesize an interface from incompatible requirements. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.
AU - Cerny, Pavol
AU - Chmelik, Martin
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
ID - 1733
IS - 3
JF - Theoretical Computer Science
TI - Interface simulation distances
VL - 560
ER -
TY - CONF
AB - Wireless sensor networks (WSNs) composed of low-power, low-cost sensor nodes are expected to form the backbone of future intelligent networks for a broad range of civil, industrial and military applications. These sensor nodes are often deployed through random spreading, and function in dynamic environments. Many applications of WSNs such as pollution tracking, forest fire detection, and military surveillance require knowledge of the location of constituent nodes. But the use of technologies such as GPS on all nodes is prohibitive due to power and cost constraints. So, the sensor nodes need to autonomously determine their locations. Most localization techniques use anchor nodes with known locations to determine the position of remaining nodes. Localization techniques have two conflicting requirements. On one hand, an ideal localization technique should be computationally simple and on the other hand, it must be resistant to attacks that compromise anchor nodes. In this paper, we propose a computationally light-weight game theoretic secure localization technique and demonstrate its effectiveness in comparison to existing techniques.
AU - Jha, Susmit
AU - Tripakis, Stavros
AU - Seshia, Sanjit
AU - Chatterjee, Krishnendu
ID - 1853
TI - Game theoretic secure localization in wireless sensor networks
ER -
TY - JOUR
AB - Unbiased high-throughput massively parallel sequencing methods have transformed the process of discovery of novel putative driver gene mutations in cancer. In chronic lymphocytic leukemia (CLL), these methods have yielded several unexpected findings, including the driver genes SF3B1, NOTCH1 and POT1. Recent analysis, utilizing down-sampling of existing datasets, has shown that the discovery process of putative drivers is far from complete across cancer. In CLL, while driver gene mutations affecting >10% of patients were efficiently discovered with previously published CLL cohorts of up to 160 samples subjected to whole exome sequencing (WES), this sample size has only 0.78 power to detect drivers affecting 5% of patients, and only 0.12 power for drivers affecting 2% of patients. These calculations emphasize the need to apply unbiased WES to larger patient cohorts.
AU - Landau, Dan
AU - Stewart, Chip
AU - Reiter, Johannes
AU - Lawrence, Michael
AU - Sougnez, Carrie
AU - Brown, Jennifer
AU - Lopez Guillermo, Armando
AU - Gabriel, Stacey
AU - Lander, Eric
AU - Neuberg, Donna
AU - López Otín, Carlos
AU - Campo, Elias
AU - Getz, Gad
AU - Wu, Catherine
ID - 1884
IS - 21
JF - Blood
TI - Novel putative driver gene mutations in chronic lymphocytic leukemia (CLL): results from a combined analysis of whole exome sequencing of 262 primary CLL aamples
VL - 124
ER -
TY - CONF
AB - We consider two-player zero-sum partial-observation stochastic games on graphs. Based on the information available to the players these games can be classified as follows: (a) general partial-observation (both players have partial view of the game); (b) one-sided partial-observation (one player has partial-observation and the other player has complete-observation); and (c) perfect-observation (both players have complete view of the game). The one-sided partial-observation games subsumes the important special case of one-player partial-observation stochastic games (or partial-observation Markov decision processes (POMDPs)). Based on the randomization available for the strategies, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. We consider all these classes of games with reachability, and parity objectives that can express all ω-regular objectives. The analysis problems are classified into the qualitative analysis that asks for the existence of a strategy that ensures the objective with probability 1; and the quantitative analysis that asks for the existence of a strategy that ensures the objective with probability at least λ (0,1). In this talk we will cover a wide range of results: for perfect-observation games; for POMDPs; for one-sided partial-observation games; and for general partial-observation games.
AU - Chatterjee, Krishnendu
ID - 1903
IS - PART 1
TI - Partial-observation stochastic reachability and parity games
VL - 8634
ER -
TY - CONF
AB - We present a general framework for applying machine-learning algorithms to the verification of Markov decision processes (MDPs). The primary goal of these techniques is to improve performance by avoiding an exhaustive exploration of the state space. Our framework focuses on probabilistic reachability, which is a core property for verification, and is illustrated through two distinct instantiations. The first assumes that full knowledge of the MDP is available, and performs a heuristic-driven partial exploration of the model, yielding precise lower and upper bounds on the required probability. The second tackles the case where we may only sample the MDP, and yields probabilistic guarantees, again in terms of both the lower and upper bounds, which provides efficient stopping criteria for the approximation. The latter is the first extension of statistical model checking for unbounded properties inMDPs. In contrast with other related techniques, our approach is not restricted to time-bounded (finite-horizon) or discounted properties, nor does it assume any particular properties of the MDP. We also show how our methods extend to LTL objectives. We present experimental results showing the performance of our framework on several examples.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Forejt, Vojtěch
AU - Kretinsky, Jan
AU - Kwiatkowska, Marta
AU - Parker, David
AU - Ujma, Mateusz
ED - Cassez, Franck
ED - Raskin, Jean-François
ID - 2027
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Verification of markov decision processes using learning algorithms
VL - 8837
ER -
TY - JOUR
AB - Recently, there has been an effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions. At the heart of quantitative objectives lies the accumulation of values along a computation. It is often the accumulated sum, as with energy objectives, or the accumulated average, as with mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric (or Boolean) variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point in time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire infinite computation. We study the border of decidability for such quantitative extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities with both prefix-accumulation assertions, or extending LTL with both path-accumulation assertions, results in temporal logics whose model-checking problem is decidable. Moreover, the prefix-accumulation assertions may be generalized with "controlled accumulation," allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that this branching-time logic is, in a sense, the maximal logic with one or both of the prefix-accumulation assertions that permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, such as CTL or LTL, makes the problem undecidable.
AU - Boker, Udi
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Kupferman, Orna
ID - 2038
IS - 4
JF - ACM Transactions on Computational Logic (TOCL)
TI - Temporal specifications with accumulative values
VL - 15
ER -
TY - CONF
AB - A standard technique for solving the parameterized model checking problem is to reduce it to the classic model checking problem of finitely many finite-state systems. This work considers some of the theoretical power and limitations of this technique. We focus on concurrent systems in which processes communicate via pairwise rendezvous, as well as the special cases of disjunctive guards and token passing; specifications are expressed in indexed temporal logic without the next operator; and the underlying network topologies are generated by suitable Monadic Second Order Logic formulas and graph operations. First, we settle the exact computational complexity of the parameterized model checking problem for some of our concurrent systems, and establish new decidability results for others. Second, we consider the cases that model checking the parameterized system can be reduced to model checking some fixed number of processes, the number is known as a cutoff. We provide many cases for when such cutoffs can be computed, establish lower bounds on the size of such cutoffs, and identify cases where no cutoff exists. Third, we consider cases for which the parameterized system is equivalent to a single finite-state system (more precisely a Büchi word automaton), and establish tight bounds on the sizes of such automata.
AU - Aminof, Benjamin
AU - Kotek, Tomer
AU - Rubin, Sacha
AU - Spegni, Francesco
AU - Veith, Helmut
ED - Baldan, Paolo
ED - Gorla, Daniele
ID - 2052
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Parameterized model checking of rendezvous systems
VL - 8704
ER -
TY - CONF
AB - In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a longstanding open problem concerning the representation of memoryless continuous time by memoryfull continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems.
AU - Hermanns, Holger
AU - Krčál, Jan
AU - Kretinsky, Jan
ED - Baldan, Paolo
ED - Gorla, Daniele
ID - 2053
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Probabilistic bisimulation: Naturally on distributions
VL - 8704
ER -
TY - CONF
AB - We study two-player concurrent games on finite-state graphs played for an infinite number of rounds, where in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. The objectives are ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). While the qualitative analysis problem for concurrent parity games with infinite-memory, infinite-precision randomized strategies was studied before, we study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision, or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory, or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in (n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. Our symbolic algorithms are based on a characterization of the winning sets as μ-calculus formulas, however, our μ-calculus formulas are crucially different from the ones for concurrent parity games (without bounded rationality); and our memoryless witness strategy constructions are significantly different from the infinite-memory witness strategy constructions for concurrent parity games.
AU - Chatterjee, Krishnendu
ED - Baldan, Paolo
ED - Gorla, Daniele
ID - 2054
T2 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
TI - Qualitative concurrent parity games: Bounded rationality
VL - 8704
ER -
TY - CONF
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems.We focus on qualitative properties forMDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability. We introduce a new simulation relation to capture the refinement relation ofMDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.We present an automated technique for assume-guarantee style reasoning for compositional analysis ofMDPs with qualitative properties by giving a counterexample guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Daca, Przemyslaw
ID - 2063
TI - CEGAR for qualitative analysis of probabilistic systems
VL - 8559
ER -
TY - JOUR
AB - The computation of the winning set for Büchi objectives in alternating games on graphs is a central problem in computer-aided verification with a large number of applications. The long-standing best known upper bound for solving the problem is Õ(n ⋅ m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the Õ(n ⋅ m) boundary by presenting a new technique that reduces the running time to O(n2). This bound also leads to O(n2)-time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of Õ(n ⋅ m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n3)), and (3) in Markov decision processes (improving for m>n4/3 an earlier bound of O(m ⋅ √m)). We then show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. Our algorithms are the first dynamic algorithms for this problem. We then consider another core graph theoretic problem in verification of probabilistic systems, namely computing the maximal end-component decomposition of a graph. We present two improved static algorithms for the maximal end-component decomposition problem. Our first algorithm is an O(m ⋅ √m)-time algorithm, and our second algorithm is an O(n2)-time algorithm which is obtained using the same technique as for alternating Büchi games. Thus, we obtain an O(min &lcu;m ⋅ √m,n2})-time algorithm improving the long-standing O(n ⋅ m) time bound. Finally, we show how to maintain the maximal end-component decomposition of a graph under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per edge deletion, and O(m) worst-case time per edge insertion. Again, our algorithms are the first dynamic algorithms for this problem.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
ID - 2141
IS - 3
JF - Journal of the ACM
TI - Efficient and dynamic algorithms for alternating Büchi games and maximal end-component decomposition
VL - 61
ER -
TY - CONF
AB - We study two-player (zero-sum) concurrent mean-payoff games played on a finite-state graph. We focus on the important sub-class of ergodic games where all states are visited infinitely often with probability 1. The algorithmic study of ergodic games was initiated in a seminal work of Hoffman and Karp in 1966, but all basic complexity questions have remained unresolved. Our main results for ergodic games are as follows: We establish (1) an optimal exponential bound on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy); (2) the approximation problem lies in FNP; (3) the approximation problem is at least as hard as the decision problem for simple stochastic games (for which NP ∩ coNP is the long-standing best known bound). We present a variant of the strategy-iteration algorithm by Hoffman and Karp; show that both our algorithm and the classical value-iteration algorithm can approximate the value in exponential time; and identify a subclass where the value-iteration algorithm is a FPTAS. We also show that the exact value can be expressed in the existential theory of the reals, and establish square-root sum hardness for a related class of games.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 2162
IS - Part 2
TI - The complexity of ergodic mean payoff games
VL - 8573
ER -
TY - CONF
AB - We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable in general, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. From our results we derive new complexity results for partial-observation stochastic games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 2163
IS - Part 2
T2 - Lecture Notes in Computer Science
TI - Games with a weak adversary
VL - 8573
ER -
TY - JOUR
AB - Systems should not only be correct but also robust in the sense that they behave reasonably in unexpected situations. This article addresses synthesis of robust reactive systems from temporal specifications. Existing methods allow arbitrary behavior if assumptions in the specification are violated. To overcome this, we define two robustness notions, combine them, and show how to enforce them in synthesis. The first notion applies to safety properties: If safety assumptions are violated temporarily, we require that the system recovers to normal operation with as few errors as possible. The second notion requires that, if liveness assumptions are violated, as many guarantees as possible should be fulfilled nevertheless. We present a synthesis procedure achieving this for the important class of GR(1) specifications, and establish complexity bounds. We also present an implementation of a special case of robustness, and show experimental results.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Greimel, Karin
AU - Henzinger, Thomas A
AU - Hofferek, Georg
AU - Jobstmann, Barbara
AU - Könighofer, Bettina
AU - Könighofer, Robert
ID - 2187
IS - 3-4
JF - Acta Informatica
TI - Synthesizing robust systems
VL - 51
ER -
TY - CONF
AB - We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula φ. The automaton is the product of a master automaton and an array of slave automata, one for each G-subformula of φ. The slave automaton for G ψ is in charge of recognizing whether FG ψ holds. As opposed to standard determinization procedures, the states of all our automata have a clear logical structure, which allows for various optimizations. Our construction subsumes former algorithms for fragments of LTL. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.
AU - Esparza, Javier
AU - Kretinsky, Jan
ID - 2190
TI - From LTL to deterministic automata: A safraless compositional approach
VL - 8559
ER -
TY - JOUR
AB - In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states. The game is played for infinitely many rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1) or positively (i.e., with positive probability), no matter the strategy of the second player. We classify such games according to the information and to the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two-sided with (c) both players having partial observation. On the basis of randomization, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. Our main results for pure strategies are as follows: (1) For one-sided games with player 2 having perfect observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strategies are not sufficient, and we present an exponential upper bound on memory both for almost-sure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete and present symbolic algorithms that avoid the explicit exponential construction. (2) For one-sided games with player 1 having perfect observation we show that nonelementarymemory is both necessary and sufficient for both almost-sure and positive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least nonelementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence result exhibit serious flaws in previous results of the literature: we show a nonelementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 2211
IS - 2
JF - ACM Transactions on Computational Logic (TOCL)
TI - Partial-observation stochastic games: How to win when belief fails
VL - 15
ER -
TY - CONF
AB - The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 1/2-player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other transitions are determined probabilistically. We consider 2 1/2-player games where the objective of the System is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a mean-payoff condition). We establish that the problem of deciding whether the System can ensure that the probability to satisfy the mean-payoff parity objective is at least a given threshold is in NP ∩ coNP, matching the best known bound in the special case of 2-player games (where all transitions are deterministic). We present an algorithm running in time O(d·n2d·MeanGame) to compute the set of almost-sure winning states from which the objective can be ensured with probability 1, where n is the number of states of the game, d the number of priorities of the parity objective, and MeanGame is the complexity to compute the set of almost-sure winning states in 2 1/2-player mean-payoff games. Our results are useful in the synthesis of stochastic reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective).
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Oualhadj, Youssouf
ID - 2212
TI - Perfect-information stochastic mean-payoff parity games
VL - 8412
ER -
TY - CONF
AB - We consider two-player partial-observation stochastic games on finitestate graphs where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are ε-regular conditions specified as parity objectives. The qualitative-analysis problem given a partial-observation stochastic game and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). These qualitative-analysis problems are known to be undecidable. However in many applications the relevant question is the existence of finite-memory strategies, and the qualitative-analysis problems under finite-memory strategies was recently shown to be decidable in 2EXPTIME.We improve the complexity and show that the qualitative-analysis problems for partial-observation stochastic parity games under finite-memory strategies are EXPTIME-complete; and also establish optimal (exponential) memory bounds for finite-memory strategies required for qualitative analysis.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Nain, Sumit
AU - Vardi, Moshe
ID - 2213
TI - The complexity of partial-observation stochastic parity games with finite-memory strategies
VL - 8412
ER -
TY - CONF
AB - The edit distance between two (untimed) traces is the minimum cost of a sequence of edit operations (insertion, deletion, or substitution) needed to transform one trace to the other. Edit distances have been extensively studied in the untimed setting, and form the basis for approximate matching of sequences in different domains such as coding theory, parsing, and speech recognition. In this paper, we lift the study of edit distances from untimed languages to the timed setting. We define an edit distance between timed words which incorporates both the edit distance between the untimed words and the absolute difference in time stamps. Our edit distance between two timed words is computable in polynomial time. Further, we show that the edit distance between a timed word and a timed language generated by a timed automaton, defined as the edit distance between the word and the closest word in the language, is PSPACE-complete. While computing the edit distance between two timed automata is undecidable, we show that the approximate version, where we decide if the edit distance between two timed automata is either less than a given parameter or more than δ away from the parameter, for δ > 0, can be solved in exponential space and is EXPSPACE-hard. Our definitions and techniques can be generalized to the setting of hybrid systems, and analogous decidability results hold for rectangular automata.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Majumdar, Ritankar
ID - 2216
TI - Edit distance for timed automata
ER -
TY - JOUR
AB - We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with κ limit-average functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the case of one limit-average function, both randomization and memory are necessary for strategies even for ε-approximation, and that finite-memory randomized strategies are sufficient for achieving Pareto optimal values. Under the satisfaction objective, in contrast to the case of one limit-average function, infinite memory is necessary for strategies achieving a specific value (i.e. randomized finite-memory strategies are not sufficient), whereas memoryless randomized strategies are sufficient for ε-approximation, for all ε > 0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be ε-approximated in time polynomial in the size of the MDP and 1/ε, and exponential in the number of limit-average functions, for all ε > 0. Our analysis also reveals flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, corrects the flaws, and allows us to obtain improved results.
AU - Brázdil, Tomáš
AU - Brožek, Václav
AU - Chatterjee, Krishnendu
AU - Forejt, Vojtěch
AU - Kučera, Antonín
ID - 2234
IS - 1
JF - Logical Methods in Computer Science
SN - 18605974
TI - Markov decision processes with multiple long-run average objectives
VL - 10
ER -
TY - JOUR
AB - Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different classes and representations of Muller games lead to problems of varying computational complexity. One such class are parity games; these are of particular significance in computational complexity, as they remain one of the few combinatorial problems known to be in NP ∩ co-NP but not known to be in P. We show that winning regions for a Muller game can be determined from the alternating structure of its traps. To every Muller game we then associate a natural number that we call its trap depth; this parameter measures how complicated the trap structure is. We present algorithms for parity games that run in polynomial time for graphs of bounded trap depth, and in general run in time exponential in the trap depth.
AU - Grinshpun, Andrey
AU - Phalitnonkiat, Pakawat
AU - Rubin, Sasha
AU - Tarfulea, Andrei
ID - 2246
JF - Theoretical Computer Science
SN - 03043975
TI - Alternating traps in Muller and parity games
VL - 521
ER -
TY - CONF
AB - First cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of the edges (or nodes) forming this cycle. These games are traditionally of interest because of their connection with infinite-duration games such as parity and mean-payoff games. We study the memory requirements for winning strategies of FCGs and certain associated infinite duration games. We exhibit a simple FCG that is not memoryless determined (this corrects a mistake in Memoryless determinacy of parity and mean payoff games: a simple proof by Bj⋯orklund, Sandberg, Vorobyov (2004) that claims that FCGs for which Y is closed under cyclic permutations are memoryless determined). We show that θ (n)! memory (where n is the number of nodes in the graph), which is always sufficient, may be necessary to win some FCGs. On the other hand, we identify easy to check conditions on Y (i.e., Y is closed under cyclic permutations, and both Y and its complement are closed under concatenation) that are sufficient to ensure that the corresponding FCGs and their associated infinite duration games are memoryless determined. We demonstrate that many games considered in the literature, such as mean-payoff, parity, energy, etc., satisfy these conditions. On the complexity side, we show (for efficiently computable Y) that while solving FCGs is in PSPACE, solving some families of FCGs is PSPACE-hard.
AU - Aminof, Benjamin
AU - Rubin, Sasha
ID - 475
T2 - Electronic Proceedings in Theoretical Computer Science, EPTCS
TI - First cycle games
VL - 146
ER -
TY - JOUR
AB - Energy games belong to a class of turn-based two-player infinite-duration games played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in NP∩co-NP, but are not known to be in P. The existence of polynomial-time algorithms has been a major open problem for decades and apart from pseudopolynomial algorithms there is no algorithm that solves any non-trivial subclass in polynomial time. In this paper, we give several results based on the weight structures of the graph. First, we identify a notion of penalty and present a polynomial-time algorithm when the penalty is large. Our algorithm is the first polynomial-time algorithm on a large class of weighted graphs. It includes several worst-case instances on which previous algorithms, such as value iteration and random facet algorithms, require at least sub-exponential time. Our main technique is developing the first non-trivial approximation algorithm and showing how to convert it to an exact algorithm. Moreover, we show that in a practical case in verification where weights are clustered around a constant number of values, the energy game problem can be solved in polynomial time. We also show that the problem is still as hard as in general when the clique-width is bounded or the graph is strongly ergodic, suggesting that restricting the graph structure does not necessarily help.
AU - Chatterjee, Krishnendu
AU - Henzinger, Monika
AU - Krinninger, Sebastian
AU - Nanongkai, Danupon
ID - 535
IS - 3
JF - Algorithmica
TI - Polynomial time algorithms for energy games with special weight structures
VL - 70
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Chmelik, Martin
ID - 5412
SN - 2664-1690
TI - CEGAR for qualitative analysis of probabilistic systems
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Chmelik, Martin
ID - 5413
SN - 2664-1690
TI - CEGAR for qualitative analysis of probabilistic systems
ER -
TY - GEN
AB - We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation.
We have implemented our algorithms and show that the compositional analysis leads to significant improvements.
AU - Chatterjee, Krishnendu
AU - Daca, Przemyslaw
AU - Chmelik, Martin
ID - 5414
SN - 2664-1690
TI - CEGAR for qualitative analysis of probabilistic systems
ER -
TY - GEN
AB - Recently there has been a significant effort to add quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, several basic system properties such as average response time cannot be expressed with weighted automata. In this work, we introduce nested weighted automata as a new formalism for expressing important quantitative properties such as average response time. We establish an almost complete decidability picture for the basic decision problems for nested weighted automata, and illustrate its applicability in several domains.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 5415
SN - 2664-1690
TI - Nested weighted automata
ER -
TY - GEN
AB - We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. Our results have tight connections with partial-observation stochastic games for which we derive new complexity results.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 5418
SN - 2664-1690
TI - Games with a weak adversary
ER -
TY - GEN
AB - We consider the reachability and shortest path problems on low tree-width graphs, with n nodes, m edges, and tree-width t, on a standard RAM with wordsize W. We use O to hide polynomial factors of the inverse of the Ackermann function. Our main contributions are three fold:
1. For reachability, we present an algorithm that requires O(n·t2·log(n/t)) preprocessing time, O(n·(t·log(n/t))/W) space, and O(t/W) time for pair queries and O((n·t)/W) time for single-source queries. Note that for constant t our algorithm uses O(n·logn) time for preprocessing; and O(n/W) time for single-source queries, which is faster than depth first search/breath first search (after the preprocessing).
2. We present an algorithm for shortest path that requires O(n·t2) preprocessing time, O(n·t) space, and O(t2) time for pair queries and O(n·t) time single-source queries.
3. We give a space versus query time trade-off algorithm for shortest path that, given any constant >0, requires O(n·t2) preprocessing time, O(n·t2) space, and O(n1−·t2) time for pair queries.
Our algorithms improve all existing results, and use very simple data structures.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
AU - Pavlogiannis, Andreas
ID - 5419
SN - 2664-1690
TI - Improved algorithms for reachability and shortest path on low tree-width graphs
ER -