TY - CONF
AB - A standard objective in partially-observable Markov decision processes (POMDPs) is to find a policy that maximizes the expected discounted-sum payoff. However, such policies may still permit unlikely but highly undesirable outcomes, which is problematic especially in safety-critical applications. Recently, there has been a surge of interest in POMDPs where the goal is to maximize the probability to ensure that the payoff is at least a given threshold, but these approaches do not consider any optimization beyond satisfying this threshold constraint. In this work we go beyond both the “expectation” and “threshold” approaches and consider a “guaranteed payoff optimization (GPO)” problem for POMDPs, where we are given a threshold t and the objective is to find a policy σ such that a) each possible outcome of σ yields a discounted-sum payoff of at least t, and b) the expected discounted-sum payoff of σ is optimal (or near-optimal) among all policies satisfying a). We present a practical approach to tackle the GPO problem and evaluate it on standard POMDP benchmarks.
AU - Chatterjee, Krishnendu
AU - Novotny, Petr
AU - Pérez, Guillermo
AU - Raskin, Jean
AU - Zikelic, Djordje
ID - 1009
T2 - Proceedings of the 31st AAAI Conference on Artificial Intelligence
TI - Optimizing expectation with guarantees in POMDPs
VL - 5
ER -
TY - CONF
AB - Pushdown systems (PDSs) and recursive state machines (RSMs), which are linearly equivalent, are standard models for interprocedural analysis. Yet RSMs are more convenient as they (a) explicitly model function calls and returns, and (b) specify many natural parameters for algorithmic analysis, e.g., the number of entries and exits. We consider a general framework where RSM transitions are labeled from a semiring and path properties are algebraic with semiring operations, which can model, e.g., interprocedural reachability and dataflow analysis problems. Our main contributions are new algorithms for several fundamental problems. As compared to a direct translation of RSMs to PDSs and the best-known existing bounds of PDSs, our analysis algorithm improves the complexity for finite-height semirings (that subsumes reachability and standard dataflow properties). We further consider the problem of extracting distance values from the representation structures computed by our algorithm, and give efficient algorithms that distinguish the complexity of a one-time preprocessing from the complexity of each individual query. Another advantage of our algorithm is that our improvements carry over to the concurrent setting, where we improve the bestknown complexity for the context-bounded analysis of concurrent RSMs. Finally, we provide a prototype implementation that gives a significant speed-up on several benchmarks from the SLAM/SDV project.
AU - Chatterjee, Krishnendu
AU - Kragl, Bernhard
AU - Mishra, Samarth
AU - Pavlogiannis, Andreas
ED - Yang, Hongseok
ID - 1011
SN - 03029743
TI - Faster algorithms for weighted recursive state machines
VL - 10201
ER -
TY - JOUR
AB - We consider the problem of reachability in pushdown graphs. We study the problem for pushdown graphs with constant treewidth. Even for pushdown graphs with treewidth 1, for the reachability problem we establish the following: (i) the problem is PTIME-complete, and (ii) any subcubic algorithm for the problem would contradict the k-clique conjecture and imply faster combinatorial algorithms for cliques in graphs.
AU - Chatterjee, Krishnendu
AU - Osang, Georg F
ID - 1065
JF - Information Processing Letters
SN - 00200190
TI - Pushdown reachability with constant treewidth
VL - 122
ER -
TY - JOUR
AB - Simulation is an attractive alternative to language inclusion for automata as it is an under-approximation of language inclusion, but usually has much lower complexity. Simulation has also been extended in two orthogonal directions, namely, (1) fair simulation, for simulation over specified set of infinite runs; and (2) quantitative simulation, for simulation between weighted automata. While fair trace inclusion is PSPACE-complete, fair simulation can be computed in polynomial time. For weighted automata, the (quantitative) language inclusion problem is undecidable in general, whereas the (quantitative) simulation reduces to quantitative games, which admit pseudo-polynomial time algorithms.
In this work, we study (quantitative) simulation for weighted automata with Büchi acceptance conditions, i.e., we generalize fair simulation from non-weighted automata to weighted automata. We show that imposing Büchi acceptance conditions on weighted automata changes many fundamental properties of the simulation games, yet they still admit pseudo-polynomial time algorithms.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
AU - Velner, Yaron
ID - 1066
IS - 2
JF - Information and Computation
TI - Quantitative fair simulation games
VL - 254
ER -
TY - JOUR
AB - Reconstructing the evolutionary history of metastases is critical for understanding their basic biological principles and has profound clinical implications. Genome-wide sequencing data has enabled modern phylogenomic methods to accurately dissect subclones and their phylogenies from noisy and impure bulk tumour samples at unprecedented depth. However, existing methods are not designed to infer metastatic seeding patterns. Here we develop a tool, called Treeomics, to reconstruct the phylogeny of metastases and map subclones to their anatomic locations. Treeomics infers comprehensive seeding patterns for pancreatic, ovarian, and prostate cancers. Moreover, Treeomics correctly disambiguates true seeding patterns from sequencing artifacts; 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumour heterogeneity among distinct samples. In silico benchmarking on simulated tumour phylogenies across a wide range of sample purities (15–95%) and sequencing depths (25-800 × ) demonstrates the accuracy of Treeomics compared with existing methods.
AU - Reiter, Johannes
AU - Makohon Moore, Alvin
AU - Gerold, Jeffrey
AU - Božić, Ivana
AU - Chatterjee, Krishnendu
AU - Iacobuzio Donahue, Christine
AU - Vogelstein, Bert
AU - Nowak, Martin
ID - 1080
JF - Nature Communications
SN - 20411723
TI - Reconstructing metastatic seeding patterns of human cancers
VL - 8
ER -
TY - CONF
AB - Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples.
AU - Chatterjee, Krishnendu
AU - Novotny, Petr
AU - Zikelic, Djordje
ID - 1194
IS - 1
SN - 07308566
TI - Stochastic invariants for probabilistic termination
VL - 52
ER -
TY - CONF
AB - Two-player games on graphs are widely studied in formal methods as they model the interaction between a system and its environment. The game is played by moving a token throughout a graph to produce an infinite path. There are several common modes to determine how the players move the token through the graph; e.g., in turn-based games the players alternate turns in moving the token. We study the bidding mode of moving the token, which, to the best of our knowledge, has never been studied in infinite-duration games. Both players have separate budgets, which sum up to $1$. In each turn, a bidding takes place. Both players submit bids simultaneously, and a bid is legal if it does not exceed the available budget. The winner of the bidding pays his bid to the other player and moves the token. For reachability objectives, repeated bidding games have been studied and are called Richman games. There, a central question is the existence and computation of threshold budgets; namely, a value t\in [0,1] such that if\PO's budget exceeds $t$, he can win the game, and if\PT's budget exceeds 1-t, he can win the game. We focus on parity games and mean-payoff games. We show the existence of threshold budgets in these games, and reduce the problem of finding them to Richman games. We also determine the strategy-complexity of an optimal strategy. Our most interesting result shows that memoryless strategies suffice for mean-payoff bidding games.
AU - Avni, Guy
AU - Henzinger, Thomas A
AU - Chonev, Ventsislav K
ID - 950
SN - 1868-8969
TI - Infinite-duration bidding games
VL - 85
ER -
TY - CONF
AB - The notion of treewidth of graphs has been exploited for faster algorithms for several problems arising in verification and program analysis. Moreover, various notions of balanced tree decompositions have been used for improved algorithms supporting dynamic updates and analysis of concurrent programs. In this work, we present a tool for constructing tree-decompositions of CFGs obtained from Java methods, which is implemented as an extension to the widely used Soot framework. The experimental results show that our implementation on real-world Java benchmarks is very efficient. Our tool also provides the first implementation for balancing tree-decompositions. In summary, we present the first tool support for exploiting treewidth in the static analysis problems on Java programs.
AU - Chatterjee, Krishnendu
AU - Goharshady, Amir
AU - Pavlogiannis, Andreas
ED - D'Souza, Deepak
ID - 949
SN - 03029743
TI - JTDec: A tool for tree decompositions in soot
VL - 10482
ER -
TY - CONF
AB - We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of non-recursive programs. First, we apply ranking functions to recursion, resulting in measure functions, and show that they provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in non-polynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas’ Lemma, and Handelman’s Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form O(n log n) as well as O(nr) where r is not an integer. We present experimental results to demonstrate that our approach can efficiently obtain worst-case bounds of classical recursive algorithms such as Merge-Sort, Closest-Pair, Karatsuba’s algorithm and Strassen’s algorithm.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Goharshady, Amir
ED - Majumdar, Rupak
ED - Kunčak, Viktor
ID - 639
SN - 978-331963389-3
TI - Non-polynomial worst case analysis of recursive programs
VL - 10427
ER -
TY - CONF
AB - Magic: the Gathering is a game about magical combat for any number of players. Formally it is a zero-sum, imperfect information stochastic game that consists of a potentially unbounded number of steps. We consider the problem of deciding if a move is legal in a given single step of Magic. We show that the problem is (a) coNP-complete in general; and (b) in P if either of two small sets of cards are not used. Our lower bound holds even for single-player Magic games. The significant aspects of our results are as follows: First, in most real-life game problems, the task of deciding whether a given move is legal in a single step is trivial, and the computationally hard task is to find the best sequence of legal moves in the presence of multiple players. In contrast, quite uniquely our hardness result holds for single step and with only one-player. Second, we establish efficient algorithms for important special cases of Magic.
AU - Chatterjee, Krishnendu
AU - Ibsen-Jensen, Rasmus
ID - 478
TI - The complexity of deciding legality of a single step of magic: The gathering
VL - 285
ER -
TY - CONF
AB - Graph games provide the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic reactive processes, the traditional model is perfect-information stochastic games, where some transitions of the game graph are controlled by two adversarial players, and the other transitions are executed probabilistically. We consider such games where the objective is the conjunction of several quantitative objectives (specified as mean-payoff conditions), which we refer to as generalized mean-payoff objectives. The basic decision problem asks for the existence of a finite-memory strategy for a player that ensures the generalized mean-payoff objective be satisfied with a desired probability against all strategies of the opponent. A special case of the decision problem is the almost-sure problem where the desired probability is 1. Previous results presented a semi-decision procedure for -approximations of the almost-sure problem. In this work, we show that both the almost-sure problem as well as the general basic decision problem are coNP-complete, significantly improving the previous results. Moreover, we show that in the case of 1-player stochastic games, randomized memoryless strategies are sufficient and the problem can be solved in polynomial time. In contrast, in two-player stochastic games, we show that even with randomized strategies exponential memory is required in general, and present a matching exponential upper bound. We also study the basic decision problem with infinite-memory strategies and present computational complexity results for the problem. Our results are relevant in the synthesis of stochastic reactive systems with multiple quantitative requirements.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 480
TI - Perfect-information stochastic games with generalized mean-payoff objectives
VL - 05-08-July-2016
ER -
TY - GEN
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 - 5445
SN - 2664-1690
TI - Quantitative interprocedural analysis
ER -
TY - GEN
AB - The fixation probability is the probability that a new mutant introduced in a homogeneous population eventually takes over the entire population.
The fixation probability is a fundamental quantity of natural selection, and known to depend on the population structure.
Amplifiers of natural selection are population structures which increase the fixation probability of advantageous mutants, as compared to the baseline case of well-mixed populations. In this work we focus on symmetric population structures represented as undirected graphs. In the regime of undirected graphs, the strongest amplifier known has been the Star graph, and the existence of undirected graphs with stronger amplification properties has remained open for over a decade.
In this work we present the Comet and Comet-swarm families of undirected graphs. We show that for a range of fitness values of the mutants, the Comet and Comet-swarm graphs have fixation probability strictly larger than the fixation probability of the Star graph, for fixed population size and at the limit of large populations, respectively.
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 5449
SN - 2664-1690
TI - Amplification on undirected population structures: Comets beat stars
ER -
TY - GEN
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 5451
SN - 2664-1690
TI - Strong amplifiers of natural selection
ER -
TY - GEN
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 5452
SN - 2664-1690
TI - Arbitrarily strong amplifiers of natural selection
ER -
TY - GEN
AU - Pavlogiannis, Andreas
AU - Tkadlec, Josef
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 5453
SN - 2664-1690
TI - Arbitrarily strong amplifiers of natural selection
ER -
TY - JOUR
AB - Direct reciprocity is a major mechanism for the evolution of cooperation. Several classical studies have suggested that humans should quickly learn to adopt reciprocal strategies to establish mutual cooperation in repeated interactions. On the other hand, the recently discovered theory of ZD strategies has found that subjects who use extortionate strategies are able to exploit and subdue cooperators. Although such extortioners have been predicted to succeed in any population of adaptive opponents, theoretical follow-up studies questioned whether extortion can evolve in reality. However, most of these studies presumed that individuals have similar strategic possibilities and comparable outside options, whereas asymmetries are ubiquitous in real world applications. Here we show with a model and an economic experiment that extortionate strategies readily emerge once subjects differ in their strategic power. Our experiment combines a repeated social dilemma with asymmetric partner choice. In our main treatment there is one randomly chosen group member who is unilaterally allowed to exchange one of the other group members after every ten rounds of the social dilemma. We find that this asymmetric replacement opportunity generally promotes cooperation, but often the resulting payoff distribution reflects the underlying power structure. Almost half of the subjects in a better strategic position turn into extortioners, who quickly proceed to exploit their peers. By adapting their cooperation probabilities consistent with ZD theory, extortioners force their co-players to cooperate without being similarly cooperative themselves. Comparison to non-extortionate players under the same conditions indicates a substantial net gain to extortion. Our results thus highlight how power asymmetries can endanger mutually beneficial interactions, and transform them into exploitative relationships. In particular, our results indicate that the extortionate strategies predicted from ZD theory could play a more prominent role in our daily interactions than previously thought.
AU - Hilbe, Christian
AU - Hagel, Kristin
AU - Milinski, Manfred
ID - 1322
IS - 10
JF - PLoS One
TI - Asymmetric power boosts extortion in an economic experiment
VL - 11
ER -
TY - CONF
AB - DEC-POMDPs extend POMDPs to a multi-agent setting, where several agents operate in an uncertain environment independently to achieve a joint objective. DEC-POMDPs have been studied with finite-horizon and infinite-horizon discounted-sum objectives, and there exist solvers both for exact and approximate solutions. In this work we consider Goal-DEC-POMDPs, where given a set of target states, the objective is to ensure that the target set is reached with minimal cost. We consider the indefinite-horizon (infinite-horizon with either discounted-sum, or undiscounted-sum, where absorbing goal states have zero-cost) problem. We present a new and novel method to solve the problem that extends methods for finite-horizon DEC-POMDPs and the RTDP-Bel approach for POMDPs. We present experimental results on several examples, and show that our approach presents promising results. Copyright
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
ID - 1324
T2 - Proceedings of the Twenty-Sixth International Conference on International Conference on Automated Planning and Scheduling
TI - Indefinite-horizon reachability in Goal-DEC-POMDPs
VL - 2016-January
ER -
TY - CONF
AB - We study graphs and two-player games in which rewards are assigned to states, and the goal of the players is to satisfy or dissatisfy certain property of the generated outcome, given as a mean payoff property. Since the notion of mean-payoff does not reflect possible fluctuations from the mean-payoff along a run, we propose definitions and algorithms for capturing the stability of the system, and give algorithms for deciding if a given mean payoff and stability objective can be ensured in the system.
AU - Brázdil, Tomáš
AU - Forejt, Vojtěch
AU - Kučera, Antonín
AU - Novotny, Petr
ID - 1325
TI - Stability in graphs and games
VL - 59
ER -
TY - CONF
AB - Energy Markov Decision Processes (EMDPs) are finite-state Markov decision processes where each transition is assigned an integer counter update and a rational payoff. An EMDP configuration is a pair s(n), where s is a control state and n is the current counter value. The configurations are changed by performing transitions in the standard way. We consider the problem of computing a safe strategy (i.e., a strategy that keeps the counter non-negative) which maximizes the expected mean payoff.
AU - Brázdil, Tomáš
AU - Kučera, Antonín
AU - Novotny, Petr
ID - 1326
TI - Optimizing the expected mean payoff in Energy Markov Decision Processes
VL - 9938
ER -
TY - CONF
AB - We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize the expected total cost until the target set is reached. We extend the traditional framework of POMDPs to model energy consumption, which represents a hard constraint. The energy levels may increase and decrease with transitions, and the hard constraint requires that the energy level must remain positive in all steps till the target is reached. First, we present a novel algorithm for solving POMDPs with energy levels, developing on existing POMDP solvers and using RTDP as its main method. Our second contribution is related to policy representation. For larger POMDP instances the policies computed by existing solvers are too large to be understandable. We present an automated procedure based on machine learning techniques that automatically extracts important decisions of the policy allowing us to compute succinct human readable policies. Finally, we show experimentally that our algorithm performs well and computes succinct policies on a number of POMDP instances from the literature that were naturally enhanced with energy levels.
AU - Brázdil, Tomáš
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Anchit
AU - Novotny, Petr
ID - 1327
T2 - Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems
TI - Stochastic shortest path with energy constraints in POMDPs
ER -
TY - JOUR
AB - Social dilemmas force players to balance between personal and collective gain. In many dilemmas, such as elected governments negotiating climate-change mitigation measures, the decisions are made not by individual players but by their representatives. However, the behaviour of representatives in social dilemmas has not been investigated experimentally. Here inspired by the negotiations for greenhouse-gas emissions reductions, we experimentally study a collective-risk social dilemma that involves representatives deciding on behalf of their fellow group members. Representatives can be re-elected or voted out after each consecutive collective-risk game. Selfish players are preferentially elected and are hence found most frequently in the "representatives" treatment. Across all treatments, we identify the selfish players as extortioners. As predicted by our mathematical model, their steadfast strategies enforce cooperation from fair players who finally compensate almost completely the deficit caused by the extortionate co-players. Everybody gains, but the extortionate representatives and their groups gain the most.
AU - Milinski, Manfred
AU - Hilbe, Christian
AU - Semmann, Dirk
AU - Sommerfeld, Ralf
AU - Marotzke, Jochem
ID - 1333
JF - Nature Communications
TI - Humans choose representatives who enforce cooperation in social dilemmas through extortion
VL - 7
ER -
TY - CONF
AB - In this paper we review various automata-theoretic formalisms for expressing quantitative properties. We start with finite-state Boolean automata that express the traditional regular properties. We then consider weighted ω-automata that can measure the average density of events, which finite-state Boolean automata cannot. However, even weighted ω-automata cannot express basic performance properties like average response time. We finally consider two formalisms of weighted ω-automata with monitors, where the monitors are either (a) counters or (b) weighted automata themselves. We present a translation result to establish that these two formalisms are equivalent. Weighted ω-automata with monitors generalize weighted ω-automata, and can express average response time property. They present a natural, robust, and expressive framework for quantitative specifications, with important decidable properties.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Otop, Jan
ID - 1335
TI - Quantitative monitor automata
VL - 9837
ER -
TY - CONF
AB - We study repeated games with absorbing states, a type of two-player, zero-sum concurrent mean-payoff games with the prototypical example being the Big Match of Gillete (1957). These games may not allow optimal strategies but they always have ε-optimal strategies. In this paper we design ε-optimal strategies for Player 1 in these games that use only O(log log T) space. Furthermore, we construct strategies for Player 1 that use space s(T), for an arbitrary small unbounded non-decreasing function s, and which guarantee an ε-optimal value for Player 1 in the limit superior sense. The previously known strategies use space Ω(log T) and it was known that no strategy can use constant space if it is ε-optimal even in the limit superior sense. We also give a complementary lower bound. Furthermore, we also show that no Markov strategy, even extended with finite memory, can ensure value greater than 0 in the Big Match, answering a question posed by Neyman [11].
AU - Hansen, Kristoffer
AU - Ibsen-Jensen, Rasmus
AU - Koucký, Michal
ID - 1340
TI - The big match in small space
VL - 9928
ER -
TY - JOUR
AB - We consider higher-dimensional versions of Kannan and Lipton's Orbit Problem - determining whether a target vector space V may be reached from a starting point x under repeated applications of a linear transformation A. Answering two questions posed by Kannan and Lipton in the 1980s, we show that when V has dimension one, this problem is solvable in polynomial time, and when V has dimension two or three, the problem is in NPRP.
AU - Chonev, Ventsislav K
AU - Ouaknine, Joël
AU - Worrell, James
ID - 1380
IS - 3
JF - Journal of the ACM
TI - On the complexity of the orbit problem
VL - 63
ER -
TY - CONF
AB - The continuous evolution of a wide variety of systems, including continous-time Markov chains and linear hybrid automata, can be
described in terms of linear differential equations. In this paper we study the decision problem of whether the solution x(t) of a system of linear differential equations dx/dt = Ax reaches a target halfspace infinitely often. This recurrent reachability problem can
equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function f:R≥0 --> R satisfying a given linear
differential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most 7, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order 9 (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision.
AU - Chonev, Ventsislav K
AU - Ouaknine, Joël
AU - Worrell, James
ID - 1389
T2 - LICS '16
TI - On recurrent reachability for continuous linear dynamical systems
ER -
TY - THES
AB - We study partially observable Markov decision processes (POMDPs) with objectives used in verification and artificial intelligence. The qualitative analysis problem given a POMDP and an objective asks whether there is a strategy (policy) to ensure that the objective is satisfied almost surely (with probability 1), resp. with positive probability (with probability greater than 0). For POMDPs with limit-average payoff, where a reward value in the interval [0,1] is associated to 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 limit-average constraint defines the set of paths where the payoff is at least a given threshold L1 = 1. Our main results for qualitative limit-average constraint under almost-sure winning 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 limit-average constraints we show that the problem of deciding the existence of a finite-memory controller is undecidable. We present a prototype implementation of our EXPTIME algorithm. For POMDPs with w-regular conditions specified as parity objectives, while the qualitative analysis problems are known to be undecidable even for very special case of parity objectives, we establish decidability (with optimal complexity) of the qualitative analysis problems for POMDPs with parity objectives under finite-memory strategies. We establish optimal (exponential) memory bounds and EXPTIME-completeness of the qualitative analysis problems under finite-memory strategies for POMDPs with parity objectives. Based on our theoretical algorithms we also present a practical approach, where we design heuristics to deal with the exponential complexity, and have applied our implementation on a number of well-known POMDP examples for robotics applications. For POMDPs with a set of target states and an integer cost associated with every transition, we study the optimization objective that asks to minimize the expected total cost of reaching a state in the target set, while ensuring that the target set is reached almost surely. We show that for general 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, both double and exponential in the POMDP state space size; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation algorithms that extend existing algorithms for POMDPs with finite-horizon objectives. We show experimentally that it performs well in many examples of interest. We study more deeply the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a strategy to ensure that the target set is reached almost surely. While in general the problem EXPTIME-complete, in many practical cases strategies 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. 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. Decentralized POMDPs (DEC-POMDPs) extend POMDPs to a multi-agent setting, where several agents operate in an uncertain environment independently to achieve a joint objective. In this work we consider Goal DEC-POMDPs, where given a set of target states, the objective is to ensure that the target set is reached with minimal cost. We consider the indefinite-horizon (infinite-horizon with either discounted-sum, or undiscounted-sum, where absorbing goal states have zero-cost) problem. We present a new and novel method to solve the problem that extends methods for finite-horizon DEC-POMDPs and the real-time dynamic programming approach for POMDPs. We present experimental results on several examples, and show that our approach presents promising results. In the end we present a short summary of a few other results related to verification of MDPs and POMDPs.
AU - Chmelik, Martin
ID - 1397
TI - Algorithms for partially observable markov decision processes
ER -
TY - JOUR
AB - Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player's previous move, and memory-one strategies, which take into account the own and the co-player's previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.
AU - Baek, Seung
AU - Jeong, Hyeongchai
AU - Hilbe, Christian
AU - Nowak, Martin
ID - 1423
JF - Scientific Reports
TI - Comparing reactive and memory-one strategies of direct reciprocity
VL - 6
ER -
TY - JOUR
AB - Brood parasites exploit their host in order to increase their own fitness. Typically, this results in an arms race between parasite trickery and host defence. Thus, it is puzzling to observe hosts that accept parasitism without any resistance. The ‘mafia’ hypothesis suggests that these hosts accept parasitism to avoid retaliation. Retaliation has been shown to evolve when the hosts condition their response to mafia parasites, who use depredation as a targeted response to rejection. However, it is unclear if acceptance would also emerge when ‘farming’ parasites are present in the population. Farming parasites use depredation to synchronize the timing with the host, destroying mature clutches to force the host to re-nest. Herein, we develop an evolutionary model to analyse the interaction between depredatory parasites and their hosts. We show that coevolutionary cycles between farmers and mafia can still induce host acceptance of brood parasites. However, this equilibrium is unstable and in the long-run the dynamics of this host–parasite interaction exhibits strong oscillations: when farmers are the majority, accepters conditional to mafia (the host will reject first and only accept after retaliation by the parasite) have a higher fitness than unconditional accepters (the host always accepts parasitism). This leads to an increase in mafia parasites’ fitness and in turn induce an optimal environment for accepter hosts.
AU - Chakra, Maria
AU - Hilbe, Christian
AU - Traulsen, Arne
ID - 1426
IS - 5
JF - Royal Society Open Science
TI - Coevolutionary interactions between farmers and mafia induce host acceptance of avian brood parasites
VL - 3
ER -
TY - CONF
AB - In this paper, we consider termination of probabilistic programs with real-valued variables. The questions concerned are: (a) qualitative ones that ask (i) whether the program terminates with probability 1 (almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); (b) quantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) to compute a bound B such that the probability to terminate after B steps decreases exponentially (concentration problem). To solve these questions, we utilize the notion of ranking supermartingales which is a powerful approach for proving termination of probabilistic programs. In detail, we focus on algorithmic synthesis of linear ranking-supermartingales over affine probabilistic programs (APP's) with both angelic and demonic non-determinism. An important subclass of APP's is LRAPP which is defined as the class of all APP's over which a linear ranking-supermartingale exists. Our main contributions are as follows. Firstly, we show that the membership problem of LRAPP (i) can be decided in polynomial time for APP's with at most demonic non-determinism, and (ii) is NP-hard and in PSPACE for APP's with angelic non-determinism; moreover, the NP-hardness result holds already for APP's without probability and demonic non-determinism. Secondly, we show that the concentration problem over LRAPP can be solved in the same complexity as for the membership problem of LRAPP. Finally, we show that the expectation problem over LRAPP can be solved in 2EXPTIME and is PSPACE-hard even for APP's without probability and non-determinism (i.e., deterministic programs). Our experimental results demonstrate the effectiveness of our approach to answer the qualitative and quantitative questions over APP's with at most demonic non-determinism.
AU - Chatterjee, Krishnendu
AU - Fu, Hongfei
AU - Novotny, Petr
AU - Hasheminezhad, Rouzbeh
ID - 1438
TI - Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs
VL - 20-22
ER -
TY - JOUR
AB - We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The class of ω-regular languages provides a robust specification language to express properties in verification, and parity objectives are canonical forms to express them. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). While the qualitative analysis problems are undecidable even for special cases of parity objectives, we establish decidability (with optimal complexity) for POMDPs with all parity objectives under finite-memory strategies. We establish optimal (exponential) memory bounds and EXPTIME-completeness of the qualitative analysis problems under finite-memory strategies for POMDPs with parity objectives. We also present a practical approach, where we design heuristics to deal with the exponential complexity, and have applied our implementation on a number of POMDP examples.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Tracol, Mathieu
ID - 1477
IS - 5
JF - Journal of Computer and System Sciences
TI - What is decidable about partially observable Markov decision processes with ω-regular objectives
VL - 82
ER -
TY - JOUR
AB - The inference of demographic history from genome data is hindered by a lack of efficient computational approaches. In particular, it has proved difficult to exploit the information contained in the distribution of genealogies across the genome. We have previously shown that the generating function (GF) of genealogies can be used to analytically compute likelihoods of demographic models from configurations of mutations in short sequence blocks (Lohse et al. 2011). Although the GF has a simple, recursive form, the size of such likelihood calculations explodes quickly with the number of individuals and applications of this framework have so far been mainly limited to small samples (pairs and triplets) for which the GF can be written by hand. Here we investigate several strategies for exploiting the inherent symmetries of the coalescent. In particular, we show that the GF of genealogies can be decomposed into a set of equivalence classes that allows likelihood calculations from nontrivial samples. Using this strategy, we automated blockwise likelihood calculations for a general set of demographic scenarios in Mathematica. These histories may involve population size changes, continuous migration, discrete divergence, and admixture between multiple populations. To give a concrete example, we calculate the likelihood for a model of isolation with migration (IM), assuming two diploid samples without phase and outgroup information. We demonstrate the new inference scheme with an analysis of two individual butterfly genomes from the sister species Heliconius melpomene rosina and H. cydno.
AU - Lohse, Konrad
AU - Chmelik, Martin
AU - Martin, Simon
AU - Barton, Nicholas H
ID - 1518
IS - 2
JF - Genetics
TI - Efficient strategies for calculating blockwise likelihoods under the coalescent
VL - 202
ER -
TY - JOUR
AB - We consider partially observable Markov decision processes (POMDPs) with a set of target states and an integer cost associated with every transition. The optimization objective we study asks to minimize the expected total cost of reaching a state in the target set, 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, both double exponential in the POMDP state space size; (ii) we show that the problem of approximating the optimal cost is decidable and present approximation 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 also present efficient stopping criteria for the algorithm and show experimentally that it performs well in many examples of interest.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 1529
JF - Artificial Intelligence
TI - Optimal cost almost-sure reachability in POMDPs
VL - 234
ER -
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 -