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 SN - 0014-3820 TI - Evolutionarily stable mating decisions for sequentially searching females and the stability of reproductive isolation by assortative mating VL - 69 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 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 - 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 - 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 - 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 H 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 - 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 - 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 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 - 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 - 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 - 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 - 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 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 - 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 SN - 978-3-662-47665-9 T2 - 42nd International Colloquium TI - Edit distance for pushdown automata VL - 9135 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 SN - 2663-337X TI - The subclonal evolution of cancer 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - CONF AB - We revisit the parameterized model checking problem for token-passing systems and specifications in indexed CTL  ∗ \X. Emerson and Namjoshi (1995, 2003) have shown that parameterized model checking of indexed CTL  ∗ \X in uni-directional token rings can be reduced to checking rings up to some cutoff size. Clarke et al. (2004) have shown a similar result for general topologies and indexed LTL \X, provided processes cannot choose the directions for sending or receiving the token. We unify and substantially extend these results by systematically exploring fragments of indexed CTL  ∗ \X with respect to general topologies. For each fragment we establish whether a cutoff exists, and for some concrete topologies, such as rings, cliques and stars, we infer small cutoffs. Finally, we show that the problem becomes undecidable, and thus no cutoffs exist, if processes are allowed to choose the directions in which they send or from which they receive the token. AU - Aminof, Benjamin AU - Jacobs, Swen AU - Khalimov, Ayrat AU - Rubin, Sasha ID - 10884 SN - 0302-9743 T2 - Verification, Model Checking, and Abstract Interpretation TI - Parameterized model checking of token-passing systems VL - 8318 ER - TY - JOUR AB - We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that the algorithmic question is reducible to the problem of a logarithmic number of min-plus matrix multiplications of n×n-matrices, where n is the number of vertices of the graph. (2) Second, when the weights are nonnegative, we present the first (1+ε)-approximation algorithm for the problem and the running time of our algorithm is Õ(nωlog3(nW/ε)/ε),1 where O(nω) is the time required for the classic n×n-matrix multiplication and W is the maximum value of the weights. With an additional O(log(nW/ε)) factor in space a cycle with approximately optimal weight can be computed within the same time bound. AU - Chatterjee, Krishnendu AU - Henzinger, Monika H AU - Krinninger, Sebastian AU - Loitzenbauer, Veronika AU - Raskin, Michael ID - 1375 IS - C JF - Theoretical Computer Science TI - Approximating the minimum cycle mean VL - 547 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 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 - 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 - 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 -