@inproceedings{2052,
abstract = {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.},
author = {Aminof, Benjamin and Kotek, Tomer and Rubin, Sacha and Spegni, Francesco and Veith, Helmut},
booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
editor = {Baldan, Paolo and Gorla, Daniele},
location = {Rome, Italy},
pages = {109 -- 124},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Parameterized model checking of rendezvous systems}},
doi = {10.1007/978-3-662-44584-6_9},
volume = {8704},
year = {2014},
}
@inproceedings{2053,
abstract = {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.},
author = {Hermanns, Holger and Krčál, Jan and Kretinsky, Jan},
booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
editor = {Baldan, Paolo and Gorla, Daniele},
location = {Rome, Italy},
pages = {249 -- 265},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Probabilistic bisimulation: Naturally on distributions}},
doi = {10.1007/978-3-662-44584-6_18},
volume = {8704},
year = {2014},
}
@inproceedings{2054,
abstract = {We study two-player concurrent games on finite-state graphs played for an infinite number of rounds, where in each round, the two players (player 1 and player 2) choose their moves independently and simultaneously; the current state and the two moves determine the successor state. The objectives are ω-regular winning conditions specified as parity objectives. We consider the qualitative analysis problems: the computation of the almost-sure and limit-sure winning set of states, where player 1 can ensure to win with probability 1 and with probability arbitrarily close to 1, respectively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). While the qualitative analysis problem for concurrent parity games with infinite-memory, infinite-precision randomized strategies was studied before, we study the bounded-rationality problem for qualitative analysis of concurrent parity games, where the strategy set for player 1 is restricted to bounded-resource strategies. In terms of precision, strategies can be deterministic, uniform, finite-precision, or infinite-precision; and in terms of memory, strategies can be memoryless, finite-memory, or infinite-memory. We present a precise and complete characterization of the qualitative winning sets for all combinations of classes of strategies. In particular, we show that uniform memoryless strategies are as powerful as finite-precision infinite-memory strategies, and infinite-precision memoryless strategies are as powerful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in (n2d+3) time, where n is the size of the game structure and 2d is the number of priorities (or colors), and our algorithms are symbolic. The membership problem of whether a state belongs to a winning set can be decided in NP ∩ coNP. Our symbolic algorithms are based on a characterization of the winning sets as μ-calculus formulas, however, our μ-calculus formulas are crucially different from the ones for concurrent parity games (without bounded rationality); and our memoryless witness strategy constructions are significantly different from the infinite-memory witness strategy constructions for concurrent parity games.},
author = {Chatterjee, Krishnendu},
booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
editor = {Baldan, Paolo and Gorla, Daniele},
location = {Rome, Italy},
pages = {544 -- 559},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Qualitative concurrent parity games: Bounded rationality}},
doi = {10.1007/978-3-662-44584-6_37},
volume = {8704},
year = {2014},
}
@inproceedings{2063,
abstract = {We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems.We focus on qualitative properties forMDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability. We introduce a new simulation relation to capture the refinement relation ofMDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.We present an automated technique for assume-guarantee style reasoning for compositional analysis ofMDPs with qualitative properties by giving a counterexample guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Daca, Przemyslaw},
location = {Vienna, Austria},
pages = {473 -- 490},
publisher = {Springer},
title = {{CEGAR for qualitative analysis of probabilistic systems}},
doi = {10.1007/978-3-319-08867-9_31},
volume = {8559},
year = {2014},
}
@article{2141,
abstract = {The computation of the winning set for Büchi objectives in alternating games on graphs is a central problem in computer-aided verification with a large number of applications. The long-standing best known upper bound for solving the problem is Õ(n ⋅ m), where n is the number of vertices and m is the number of edges in the graph. We are the first to break the Õ(n ⋅ m) boundary by presenting a new technique that reduces the running time to O(n2). This bound also leads to O(n2)-time algorithms for computing the set of almost-sure winning vertices for Büchi objectives (1) in alternating games with probabilistic transitions (improving an earlier bound of Õ(n ⋅ m)), (2) in concurrent graph games with constant actions (improving an earlier bound of O(n3)), and (3) in Markov decision processes (improving for m>n4/3 an earlier bound of O(m ⋅ √m)). We then show how to maintain the winning set for Büchi objectives in alternating games under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per operation. Our algorithms are the first dynamic algorithms for this problem. We then consider another core graph theoretic problem in verification of probabilistic systems, namely computing the maximal end-component decomposition of a graph. We present two improved static algorithms for the maximal end-component decomposition problem. Our first algorithm is an O(m ⋅ √m)-time algorithm, and our second algorithm is an O(n2)-time algorithm which is obtained using the same technique as for alternating Büchi games. Thus, we obtain an O(min &lcu;m ⋅ √m,n2})-time algorithm improving the long-standing O(n ⋅ m) time bound. Finally, we show how to maintain the maximal end-component decomposition of a graph under a sequence of edge insertions or a sequence of edge deletions in O(n) amortized time per edge deletion, and O(m) worst-case time per edge insertion. Again, our algorithms are the first dynamic algorithms for this problem.},
author = {Chatterjee, Krishnendu and Henzinger, Monika},
journal = {Journal of the ACM},
number = {3},
publisher = {ACM},
title = {{Efficient and dynamic algorithms for alternating Büchi games and maximal end-component decomposition}},
doi = {10.1145/2597631},
volume = {61},
year = {2014},
}
@inproceedings{2162,
abstract = {We study two-player (zero-sum) concurrent mean-payoff games played on a finite-state graph. We focus on the important sub-class of ergodic games where all states are visited infinitely often with probability 1. The algorithmic study of ergodic games was initiated in a seminal work of Hoffman and Karp in 1966, but all basic complexity questions have remained unresolved. Our main results for ergodic games are as follows: We establish (1) an optimal exponential bound on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy); (2) the approximation problem lies in FNP; (3) the approximation problem is at least as hard as the decision problem for simple stochastic games (for which NP ∩ coNP is the long-standing best known bound). We present a variant of the strategy-iteration algorithm by Hoffman and Karp; show that both our algorithm and the classical value-iteration algorithm can approximate the value in exponential time; and identify a subclass where the value-iteration algorithm is a FPTAS. We also show that the exact value can be expressed in the existential theory of the reals, and establish square-root sum hardness for a related class of games.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus},
location = {Copenhagen, Denmark},
number = {Part 2},
pages = {122 -- 133},
publisher = {Springer},
title = {{The complexity of ergodic mean payoff games}},
doi = {10.1007/978-3-662-43951-7_11},
volume = {8573},
year = {2014},
}
@inproceedings{2163,
abstract = {We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable in general, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. From our results we derive new complexity results for partial-observation stochastic games.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
booktitle = {Lecture Notes in Computer Science},
location = {Copenhagen, Denmark},
number = {Part 2},
pages = {110 -- 121},
publisher = {Springer},
title = {{Games with a weak adversary}},
doi = {10.1007/978-3-662-43951-7_10},
volume = {8573},
year = {2014},
}
@article{2187,
abstract = {Systems should not only be correct but also robust in the sense that they behave reasonably in unexpected situations. This article addresses synthesis of robust reactive systems from temporal specifications. Existing methods allow arbitrary behavior if assumptions in the specification are violated. To overcome this, we define two robustness notions, combine them, and show how to enforce them in synthesis. The first notion applies to safety properties: If safety assumptions are violated temporarily, we require that the system recovers to normal operation with as few errors as possible. The second notion requires that, if liveness assumptions are violated, as many guarantees as possible should be fulfilled nevertheless. We present a synthesis procedure achieving this for the important class of GR(1) specifications, and establish complexity bounds. We also present an implementation of a special case of robustness, and show experimental results.},
author = {Bloem, Roderick and Chatterjee, Krishnendu and Greimel, Karin and Henzinger, Thomas A and Hofferek, Georg and Jobstmann, Barbara and Könighofer, Bettina and Könighofer, Robert},
journal = {Acta Informatica},
number = {3-4},
pages = {193 -- 220},
publisher = {Springer},
title = {{Synthesizing robust systems}},
doi = {10.1007/s00236-013-0191-5},
volume = {51},
year = {2014},
}
@inproceedings{2190,
abstract = {We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula φ. The automaton is the product of a master automaton and an array of slave automata, one for each G-subformula of φ. The slave automaton for G ψ is in charge of recognizing whether FG ψ holds. As opposed to standard determinization procedures, the states of all our automata have a clear logical structure, which allows for various optimizations. Our construction subsumes former algorithms for fragments of LTL. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.},
author = {Esparza, Javier and Kretinsky, Jan},
pages = {192 -- 208},
publisher = {Springer},
title = {{From LTL to deterministic automata: A safraless compositional approach}},
doi = {10.1007/978-3-319-08867-9_13},
volume = {8559},
year = {2014},
}
@article{2211,
abstract = {In two-player finite-state stochastic games of partial observation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distribution over the successor states. The game is played for infinitely many rounds and thus the players construct an infinite path in the graph. We consider reachability objectives where the first player tries to ensure a target state to be visited almost-surely (i.e., with probability 1) or positively (i.e., with positive probability), no matter the strategy of the second player. We classify such games according to the information and to the power of randomization available to the players. On the basis of information, the game can be one-sided with either (a) player 1, or (b) player 2 having partial observation (and the other player has perfect observation), or two-sided with (c) both players having partial observation. On the basis of randomization, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. Our main results for pure strategies are as follows: (1) For one-sided games with player 2 having perfect observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strategies are not sufficient, and we present an exponential upper bound on memory both for almost-sure and positive winning strategies; we show that the problem of deciding the existence of almost-sure and positive winning strategies for player 1 is EXPTIME-complete and present symbolic algorithms that avoid the explicit exponential construction. (2) For one-sided games with player 1 having perfect observation we show that nonelementarymemory is both necessary and sufficient for both almost-sure and positive winning strategies. (3) We show that for the general (two-sided) case finite-memory strategies are sufficient for both positive and almost-sure winning, and at least nonelementary memory is required. We establish the equivalence of the almost-sure winning problems for pure strategies and for randomized strategies with actions invisible. Our equivalence result exhibit serious flaws in previous results of the literature: we show a nonelementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
journal = {ACM Transactions on Computational Logic (TOCL)},
number = {2},
publisher = {ACM},
title = {{Partial-observation stochastic games: How to win when belief fails}},
doi = {10.1145/2579821},
volume = {15},
year = {2014},
}
@inproceedings{2212,
abstract = {The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 1/2-player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other transitions are determined probabilistically. We consider 2 1/2-player games where the objective of the System is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a mean-payoff condition). We establish that the problem of deciding whether the System can ensure that the probability to satisfy the mean-payoff parity objective is at least a given threshold is in NP ∩ coNP, matching the best known bound in the special case of 2-player games (where all transitions are deterministic). We present an algorithm running in time O(d·n2d·MeanGame) to compute the set of almost-sure winning states from which the objective can be ensured with probability 1, where n is the number of states of the game, d the number of priorities of the parity objective, and MeanGame is the complexity to compute the set of almost-sure winning states in 2 1/2-player mean-payoff games. Our results are useful in the synthesis of stochastic reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective). },
author = {Chatterjee, Krishnendu and Doyen, Laurent and Gimbert, Hugo and Oualhadj, Youssouf},
location = {Grenoble, France},
pages = {210 -- 225},
publisher = {Springer},
title = {{Perfect-information stochastic mean-payoff parity games}},
doi = {10.1007/978-3-642-54830-7_14},
volume = {8412},
year = {2014},
}
@inproceedings{2213,
abstract = {We consider two-player partial-observation stochastic games on finitestate graphs where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are ε-regular conditions specified as parity objectives. The qualitative-analysis problem given a partial-observation stochastic game and a parity objective asks whether there is a strategy to ensure that the objective is satisfied with probability 1 (resp. positive probability). These qualitative-analysis problems are known to be undecidable. However in many applications the relevant question is the existence of finite-memory strategies, and the qualitative-analysis problems under finite-memory strategies was recently shown to be decidable in 2EXPTIME.We improve the complexity and show that the qualitative-analysis problems for partial-observation stochastic parity games under finite-memory strategies are EXPTIME-complete; and also establish optimal (exponential) memory bounds for finite-memory strategies required for qualitative analysis.},
author = {Chatterjee, Krishnendu and Doyen, Laurent and Nain, Sumit and Vardi, Moshe},
location = {Grenoble, France},
pages = {242 -- 257},
publisher = {Springer},
title = {{The complexity of partial-observation stochastic parity games with finite-memory strategies}},
doi = {10.1007/978-3-642-54830-7_16},
volume = {8412},
year = {2014},
}
@inproceedings{2216,
abstract = {The edit distance between two (untimed) traces is the minimum cost of a sequence of edit operations (insertion, deletion, or substitution) needed to transform one trace to the other. Edit distances have been extensively studied in the untimed setting, and form the basis for approximate matching of sequences in different domains such as coding theory, parsing, and speech recognition. In this paper, we lift the study of edit distances from untimed languages to the timed setting. We define an edit distance between timed words which incorporates both the edit distance between the untimed words and the absolute difference in time stamps. Our edit distance between two timed words is computable in polynomial time. Further, we show that the edit distance between a timed word and a timed language generated by a timed automaton, defined as the edit distance between the word and the closest word in the language, is PSPACE-complete. While computing the edit distance between two timed automata is undecidable, we show that the approximate version, where we decide if the edit distance between two timed automata is either less than a given parameter or more than δ away from the parameter, for δ > 0, can be solved in exponential space and is EXPSPACE-hard. Our definitions and techniques can be generalized to the setting of hybrid systems, and analogous decidability results hold for rectangular automata.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Majumdar, Ritankar},
location = {Berlin, Germany},
pages = {303 -- 312},
publisher = {Springer},
title = {{Edit distance for timed automata}},
doi = {10.1145/2562059.2562141},
year = {2014},
}
@article{2234,
abstract = {We study Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) functions. We consider two different objectives, namely, expectation and satisfaction objectives. Given an MDP with κ limit-average functions, in the expectation objective the goal is to maximize the expected limit-average value, and in the satisfaction objective the goal is to maximize the probability of runs such that the limit-average value stays above a given vector. We show that under the expectation objective, in contrast to the case of one limit-average function, both randomization and memory are necessary for strategies even for ε-approximation, and that finite-memory randomized strategies are sufficient for achieving Pareto optimal values. Under the satisfaction objective, in contrast to the case of one limit-average function, infinite memory is necessary for strategies achieving a specific value (i.e. randomized finite-memory strategies are not sufficient), whereas memoryless randomized strategies are sufficient for ε-approximation, for all ε > 0. We further prove that the decision problems for both expectation and satisfaction objectives can be solved in polynomial time and the trade-off curve (Pareto curve) can be ε-approximated in time polynomial in the size of the MDP and 1/ε, and exponential in the number of limit-average functions, for all ε > 0. Our analysis also reveals flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, corrects the flaws, and allows us to obtain improved results.},
author = {Brázdil, Tomáš and Brožek, Václav and Chatterjee, Krishnendu and Forejt, Vojtěch and Kučera, Antonín},
issn = {18605974},
journal = {Logical Methods in Computer Science},
number = {1},
publisher = {International Federation of Computational Logic},
title = {{Markov decision processes with multiple long-run average objectives}},
doi = {10.2168/LMCS-10(1:13)2014},
volume = {10},
year = {2014},
}
@article{2246,
abstract = {Muller games are played by two players moving a token along a graph; the winner is determined by the set of vertices that occur infinitely often. The central algorithmic problem is to compute the winning regions for the players. Different classes and representations of Muller games lead to problems of varying computational complexity. One such class are parity games; these are of particular significance in computational complexity, as they remain one of the few combinatorial problems known to be in NP ∩ co-NP but not known to be in P. We show that winning regions for a Muller game can be determined from the alternating structure of its traps. To every Muller game we then associate a natural number that we call its trap depth; this parameter measures how complicated the trap structure is. We present algorithms for parity games that run in polynomial time for graphs of bounded trap depth, and in general run in time exponential in the trap depth. },
author = {Grinshpun, Andrey and Phalitnonkiat, Pakawat and Rubin, Sasha and Tarfulea, Andrei},
issn = {03043975},
journal = {Theoretical Computer Science},
pages = {73 -- 91},
publisher = {Elsevier},
title = {{Alternating traps in Muller and parity games}},
doi = {10.1016/j.tcs.2013.11.032},
volume = {521},
year = {2014},
}
@inproceedings{475,
abstract = {First cycle games (FCG) are played on a finite graph by two players who push a token along the edges until a vertex is repeated, and a simple cycle is formed. The winner is determined by some fixed property Y of the sequence of labels of the edges (or nodes) forming this cycle. These games are traditionally of interest because of their connection with infinite-duration games such as parity and mean-payoff games. We study the memory requirements for winning strategies of FCGs and certain associated infinite duration games. We exhibit a simple FCG that is not memoryless determined (this corrects a mistake in Memoryless determinacy of parity and mean payoff games: a simple proof by Bj⋯orklund, Sandberg, Vorobyov (2004) that claims that FCGs for which Y is closed under cyclic permutations are memoryless determined). We show that θ (n)! memory (where n is the number of nodes in the graph), which is always sufficient, may be necessary to win some FCGs. On the other hand, we identify easy to check conditions on Y (i.e., Y is closed under cyclic permutations, and both Y and its complement are closed under concatenation) that are sufficient to ensure that the corresponding FCGs and their associated infinite duration games are memoryless determined. We demonstrate that many games considered in the literature, such as mean-payoff, parity, energy, etc., satisfy these conditions. On the complexity side, we show (for efficiently computable Y) that while solving FCGs is in PSPACE, solving some families of FCGs is PSPACE-hard. },
author = {Aminof, Benjamin and Rubin, Sasha},
booktitle = {Electronic Proceedings in Theoretical Computer Science, EPTCS},
location = {Grenoble, France},
pages = {83 -- 90},
publisher = {Open Publishing Association},
title = {{First cycle games}},
doi = {10.4204/EPTCS.146.11},
volume = {146},
year = {2014},
}
@article{535,
abstract = {Energy games belong to a class of turn-based two-player infinite-duration games played on a weighted directed graph. It is one of the rare and intriguing combinatorial problems that lie in NP∩co-NP, but are not known to be in P. The existence of polynomial-time algorithms has been a major open problem for decades and apart from pseudopolynomial algorithms there is no algorithm that solves any non-trivial subclass in polynomial time. In this paper, we give several results based on the weight structures of the graph. First, we identify a notion of penalty and present a polynomial-time algorithm when the penalty is large. Our algorithm is the first polynomial-time algorithm on a large class of weighted graphs. It includes several worst-case instances on which previous algorithms, such as value iteration and random facet algorithms, require at least sub-exponential time. Our main technique is developing the first non-trivial approximation algorithm and showing how to convert it to an exact algorithm. Moreover, we show that in a practical case in verification where weights are clustered around a constant number of values, the energy game problem can be solved in polynomial time. We also show that the problem is still as hard as in general when the clique-width is bounded or the graph is strongly ergodic, suggesting that restricting the graph structure does not necessarily help.},
author = {Chatterjee, Krishnendu and Henzinger, Monika and Krinninger, Sebastian and Nanongkai, Danupon},
journal = {Algorithmica},
number = {3},
pages = {457 -- 492},
publisher = {Springer},
title = {{Polynomial time algorithms for energy games with special weight structures}},
doi = {10.1007/s00453-013-9843-7},
volume = {70},
year = {2014},
}
@misc{5412,
abstract = {We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements. },
author = {Chatterjee, Krishnendu and Daca, Przemyslaw and Chmelik, Martin},
issn = {2664-1690},
pages = {31},
publisher = {IST Austria},
title = {{CEGAR for qualitative analysis of probabilistic systems}},
doi = {10.15479/AT:IST-2014-153-v1-1},
year = {2014},
}
@misc{5413,
abstract = {We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation. We have implemented our algorithms and show that the compositional analysis leads to significant improvements. },
author = {Chatterjee, Krishnendu and Daca, Przemyslaw and Chmelik, Martin},
issn = {2664-1690},
pages = {33},
publisher = {IST Austria},
title = {{CEGAR for qualitative analysis of probabilistic systems}},
doi = {10.15479/AT:IST-2014-153-v2-2},
year = {2014},
}
@misc{5414,
abstract = {We consider Markov decision processes (MDPs) which are a standard model for probabilistic systems. We focus on qualitative properties for MDPs that can express that desired behaviors of the system arise almost-surely (with probability 1) or with positive probability.
We introduce a new simulation relation to capture the refinement relation of MDPs with respect to qualitative properties, and present discrete graph theoretic algorithms with quadratic complexity to compute the simulation relation.
We present an automated technique for assume-guarantee style reasoning for compositional analysis of MDPs with qualitative properties by giving a counter-example guided abstraction-refinement approach to compute our new simulation relation.
We have implemented our algorithms and show that the compositional analysis leads to significant improvements. },
author = {Chatterjee, Krishnendu and Daca, Przemyslaw and Chmelik, Martin},
issn = {2664-1690},
pages = {33},
publisher = {IST Austria},
title = {{CEGAR for qualitative analysis of probabilistic systems}},
doi = {10.15479/AT:IST-2014-153-v3-1},
year = {2014},
}
@misc{5415,
abstract = {Recently there has been a significant effort to add quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, several basic system properties such as average response time cannot be expressed with weighted automata. In this work, we introduce nested weighted automata as a new formalism for expressing important quantitative properties such as average response time. We establish an almost complete decidability picture for the basic decision problems for nested weighted automata, and illustrate its applicability in several domains. },
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {27},
publisher = {IST Austria},
title = {{Nested weighted automata}},
doi = {10.15479/AT:IST-2014-170-v1-1},
year = {2014},
}
@misc{5418,
abstract = {We consider multi-player graph games with partial-observation and parity objective. While the decision problem for three-player games with a coalition of the first and second players against the third player is undecidable, we present a decidability result for partial-observation games where the first and third player are in a coalition against the second player, thus where the second player is adversarial but weaker due to partial-observation. We establish tight complexity bounds in the case where player 1 is less informed than player 2, namely 2-EXPTIME-completeness for parity objectives. The symmetric case of player 1 more informed than player 2 is much more complicated, and we show that already in the case where player 1 has perfect observation, memory of size non-elementary is necessary in general for reachability objectives, and the problem is decidable for safety and reachability objectives. Our results have tight connections with partial-observation stochastic games for which we derive new complexity results.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
issn = {2664-1690},
pages = {18},
publisher = {IST Austria},
title = {{Games with a weak adversary}},
doi = {10.15479/AT:IST-2014-176-v1-1},
year = {2014},
}
@misc{5419,
abstract = {We consider the reachability and shortest path problems on low tree-width graphs, with n nodes, m edges, and tree-width t, on a standard RAM with wordsize W. We use O to hide polynomial factors of the inverse of the Ackermann function. Our main contributions are three fold:
1. For reachability, we present an algorithm that requires O(n·t2·log(n/t)) preprocessing time, O(n·(t·log(n/t))/W) space, and O(t/W) time for pair queries and O((n·t)/W) time for single-source queries. Note that for constant t our algorithm uses O(n·logn) time for preprocessing; and O(n/W) time for single-source queries, which is faster than depth first search/breath first search (after the preprocessing).
2. We present an algorithm for shortest path that requires O(n·t2) preprocessing time, O(n·t) space, and O(t2) time for pair queries and O(n·t) time single-source queries.
3. We give a space versus query time trade-off algorithm for shortest path that, given any constant >0, requires O(n·t2) preprocessing time, O(n·t2) space, and O(n1−·t2) time for pair queries.
Our algorithms improve all existing results, and use very simple data structures.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {34},
publisher = {IST Austria},
title = {{Improved algorithms for reachability and shortest path on low tree-width graphs}},
doi = {10.15479/AT:IST-2014-187-v1-1},
year = {2014},
}
@misc{5420,
abstract = {We consider concurrent mean-payoff games, a very well-studied class of two-player (player 1 vs player 2) zero-sum games on finite-state graphs where every transition is assigned a reward between 0 and 1, and the payoff function is the long-run average of the rewards. The value is the maximal expected payoff that player 1 can guarantee against all strategies of player 2. We consider the computation of the set of states with value 1 under finite-memory strategies for player 1, and our main results for the problem are as follows: (1) we present a polynomial-time algorithm; (2) we show that whenever there is a finite-memory strategy, there is a stationary strategy that does not need memory at all; and (3) we present an optimal bound (which is double exponential) on the patience of stationary strategies (where patience of a distribution is the inverse of the smallest positive probability and represents a complexity measure of a stationary strategy).},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus},
issn = {2664-1690},
pages = {49},
publisher = {IST Austria},
title = {{The value 1 problem for concurrent mean-payoff games}},
doi = {10.15479/AT:IST-2014-191-v1-1},
year = {2014},
}
@misc{5421,
abstract = {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. 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.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin},
issn = {2664-1690},
pages = {27},
publisher = {IST Austria},
title = {{The complexity of evolution on graphs}},
doi = {10.15479/AT:IST-2014-190-v2-2},
year = {2014},
}
@misc{5423,
abstract = {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 taskset 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 D(over), that have been proposed in the past, for various tasksets. Our experimental results reveal that none of these algorithms is universally optimal, in the sense that there are tasksets where other schedulers provide better performance. Our framework is hence a very useful design tool for selecting optimal algorithms for a given application. },
author = {Chatterjee, Krishnendu and Kössler, Alexander and Pavlogiannis, Andreas and Schmid, Ulrich},
issn = {2664-1690},
pages = {14},
publisher = {IST Austria},
title = {{A framework for automated competitive analysis of on-line scheduling of firm-deadline tasks}},
doi = {10.15479/AT:IST-2014-300-v1-1},
year = {2014},
}
@misc{5424,
abstract = {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.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Gupta, Raghav and Kanodia, Ayush},
issn = {2664-1690},
pages = {12},
publisher = {IST Austria},
title = {{Qualitative analysis of POMDPs with temporal logic specifications for robotics applications}},
doi = {10.15479/AT:IST-2014-305-v1-1},
year = {2014},
}
@misc{5426,
abstract = {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.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Gupta, Raghav and Kanodia, Ayush},
issn = {2664-1690},
pages = {10},
publisher = {IST Austria},
title = {{Qualitative analysis of POMDPs with temporal logic specifications for robotics applications}},
doi = {10.15479/AT:IST-2014-305-v2-1},
year = {2014},
}
@misc{5427,
abstract = {We consider graphs with n nodes together with their tree-decomposition that has b = O ( n ) bags and width t , on the standard RAM computational model with wordsize W = Θ (log n ) . Our contributions are two-fold: Our first contribution is an algorithm that given a graph and its tree-decomposition as input, computes a binary and balanced tree-decomposition of width at most 4 · t + 3 of the graph in O ( b ) time and space, improving a long-standing (from 1992) bound of O ( n · log n ) time for constant treewidth graphs. Our second contribution is on reachability queries for low treewidth graphs. We build on our tree-balancing algorithm and present a data-structure for graph reachability that requires O ( n · t 2 ) preprocessing time, O ( n · t ) space, and O ( d t/ log n e ) time for pair queries, and O ( n · t · log t/ log n ) time for single-source queries. For constant t our data-structure uses O ( n ) time for preprocessing, O (1) time for pair queries, and O ( n/ log n ) time for single-source queries. This is (asymptotically) optimal and is faster than DFS/BFS when answering more than a constant number of single-source queries.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {24},
publisher = {IST Austria},
title = {{Optimal tree-decomposition balancing and reachability on low treewidth graphs}},
doi = {10.15479/AT:IST-2014-314-v1-1},
year = {2014},
}
@misc{5428,
abstract = {Simulation is an attractive alternative for language inclusion for automata as it is an under-approximation of language inclusion, but usually has much lower complexity. For non-deterministic automata, while language inclusion is PSPACE-complete, simulation can be computed in polynomial time. 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. Again, 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 for mean-payoff automata and the decidability is open for discounted-sum automata, whereas the (quantitative) simulation reduce to mean-payoff games and discounted-sum 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. For example, whereas for mean-payoff and discounted-sum games, the players do not need memory to play optimally; we show in contrast that for simulation games with Büchi acceptance conditions, (i) for mean-payoff objectives, optimal strategies for both players require infinite memory in general, and (ii) for discounted-sum objectives, optimal strategies need not exist for both players. While the simulation games with Büchi acceptance conditions are more complicated (e.g., due to infinite-memory requirements for mean-payoff objectives) as compared to their counterpart without Büchi acceptance conditions, we still present pseudo-polynomial time algorithms to solve simulation games with Büchi acceptance conditions for both weighted mean-payoff and weighted discounted-sum automata.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan and Velner, Yaron},
issn = {2664-1690},
pages = {26},
publisher = {IST Austria},
title = {{Quantitative fair simulation games}},
doi = {10.15479/AT:IST-2014-315-v1-1},
year = {2014},
}
@article{2716,
abstract = {Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we study the strategy synthesis problem for games with such multi-dimensional objectives along with a parity condition, a canonical way to express ω ω -regular conditions. While in general, the winning strategies in such games may require infinite memory, for synthesis the most relevant problem is the construction of a finite-memory winning strategy (if one exists). Our main contributions are as follows. First, we show a tight exponential bound (matching upper and lower bounds) on the memory required for finite-memory winning strategies in both multi-dimensional mean-payoff and energy games along with parity objectives. This significantly improves the triple exponential upper bound for multi energy games (without parity) that could be derived from results in literature for games on vector addition systems with states. Second, we present an optimal symbolic and incremental algorithm to compute a finite-memory winning strategy (if one exists) in such games. Finally, we give a complete characterization of when finite memory of strategies can be traded off for randomness. In particular, we show that for one-dimension mean-payoff parity games, randomized memoryless strategies are as powerful as their pure finite-memory counterparts.},
author = {Chatterjee, Krishnendu and Randour, Mickael and Raskin, Jean},
journal = {Acta Informatica},
number = {3-4},
pages = {129 -- 163},
publisher = {Springer},
title = {{Strategy synthesis for multi-dimensional quantitative objectives}},
doi = {10.1007/s00236-013-0182-6},
volume = {51},
year = {2014},
}
@article{1733,
abstract = {The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces, and how to synthesize an interface from incompatible requirements. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.},
author = {Cerny, Pavol and Chmelik, Martin and Henzinger, Thomas A and Radhakrishna, Arjun},
journal = {Theoretical Computer Science},
number = {3},
pages = {348 -- 363},
publisher = {Elsevier},
title = {{Interface simulation distances}},
doi = {10.1016/j.tcs.2014.08.019},
volume = {560},
year = {2014},
}
@inproceedings{1853,
abstract = {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.},
author = {Jha, Susmit and Tripakis, Stavros and Seshia, Sanjit and Chatterjee, Krishnendu},
location = {Cambridge, USA},
pages = {85 -- 90},
publisher = {IEEE},
title = {{Game theoretic secure localization in wireless sensor networks}},
doi = {10.1109/IOT.2014.7030120},
year = {2014},
}
@article{1884,
abstract = {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.},
author = {Landau, Dan and Stewart, Chip and Reiter, Johannes and Lawrence, Michael and Sougnez, Carrie and Brown, Jennifer and Lopez Guillermo, Armando and Gabriel, Stacey and Lander, Eric and Neuberg, Donna and López Otín, Carlos and Campo, Elias and Getz, Gad and Wu, Catherine},
journal = {Blood},
number = {21},
pages = {1952 -- 1952},
publisher = {American Society of Hematology},
title = {{Novel putative driver gene mutations in chronic lymphocytic leukemia (CLL): results from a combined analysis of whole exome sequencing of 262 primary CLL aamples}},
volume = {124},
year = {2014},
}
@inproceedings{1903,
abstract = {We consider two-player zero-sum partial-observation stochastic games on graphs. Based on the information available to the players these games can be classified as follows: (a) general partial-observation (both players have partial view of the game); (b) one-sided partial-observation (one player has partial-observation and the other player has complete-observation); and (c) perfect-observation (both players have complete view of the game). The one-sided partial-observation games subsumes the important special case of one-player partial-observation stochastic games (or partial-observation Markov decision processes (POMDPs)). Based on the randomization available for the strategies, (a) the players may not be allowed to use randomization (pure strategies), or (b) they may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) they may use full randomization. We consider all these classes of games with reachability, and parity objectives that can express all ω-regular objectives. The analysis problems are classified into the qualitative analysis that asks for the existence of a strategy that ensures the objective with probability 1; and the quantitative analysis that asks for the existence of a strategy that ensures the objective with probability at least λ (0,1). In this talk we will cover a wide range of results: for perfect-observation games; for POMDPs; for one-sided partial-observation games; and for general partial-observation games.},
author = {Chatterjee, Krishnendu},
location = {Budapest, Hungary},
number = {PART 1},
pages = {1 -- 4},
publisher = {Springer},
title = {{Partial-observation stochastic reachability and parity games}},
doi = {10.1007/978-3-662-44522-8_1},
volume = {8634},
year = {2014},
}
@article{1375,
abstract = {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.},
author = {Chatterjee, Krishnendu and Henzinger, Monika and Krinninger, Sebastian and Loitzenbauer, Veronika and Raskin, Michael},
journal = {Theoretical Computer Science},
number = {C},
pages = {104 -- 116},
publisher = {Elsevier},
title = {{Approximating the minimum cycle mean}},
doi = {10.1016/j.tcs.2014.06.031},
volume = {547},
year = {2014},
}
@inproceedings{2000,
abstract = {In this work we present a flexible tool for tumor progression, which simulates the evolutionary dynamics of cancer. Tumor progression implements a multi-type branching process where the key parameters are the fitness landscape, the mutation rate, and the average time of cell division. The fitness of a cancer cell depends on the mutations it has accumulated. The input to our tool could be any fitness landscape, mutation rate, and cell division time, and the tool produces the growth dynamics and all relevant statistics.},
author = {Reiter, Johannes and Božić, Ivana and Chatterjee, Krishnendu and Nowak, Martin},
booktitle = {Proceedings of 25th Int. Conf. on Computer Aided Verification},
location = {St. Petersburg, Russia},
pages = {101 -- 106},
publisher = {Springer},
title = {{TTP: Tool for tumor progression}},
doi = {10.1007/978-3-642-39799-8_6},
volume = {8044},
year = {2013},
}
@inproceedings{2238,
abstract = {We study the problem of achieving a given value in Markov decision processes (MDPs) with several independent discounted reward objectives. We consider a generalised version of discounted reward objectives, in which the amount of discounting depends on the states visited and on the objective. This definition extends the usual definition of discounted reward, and allows to capture the systems in which the value of different commodities diminish at different and variable rates.
We establish results for two prominent subclasses of the problem, namely state-discount models where the discount factors are only dependent on the state of the MDP (and independent of the objective), and reward-discount models where they are only dependent on the objective (but not on the state of the MDP). For the state-discount models we use a straightforward reduction to expected total reward and show that the problem whether a value is achievable can be solved in polynomial time. For the reward-discount model we show that memory and randomisation of the strategies are required, but nevertheless that the problem is decidable and it is sufficient to consider strategies which after a certain number of steps behave in a memoryless way.
For the general case, we show that when restricted to graphs (i.e. MDPs with no randomisation), pure strategies and discount factors of the form 1/n where n is an integer, the problem is in PSPACE and finite memory suffices for achieving a given value. We also show that when the discount factors are not of the form 1/n, the memory required by a strategy can be infinite.
},
author = {Chatterjee, Krishnendu and Forejt, Vojtěch and Wojtczak, Dominik},
location = {Stellenbosch, South Africa},
pages = {228 -- 242},
publisher = {Springer},
title = {{Multi-objective discounted reward verification in graphs and MDPs}},
doi = {10.1007/978-3-642-45221-5_17},
volume = {8312},
year = {2013},
}
@article{2247,
abstract = {Cooperative behavior, where one individual incurs a cost to help another, is a wide spread phenomenon. Here we study direct reciprocity in the context of the alternating Prisoner's Dilemma. We consider all strategies that can be implemented by one and two-state automata. We calculate the payoff matrix of all pairwise encounters in the presence of noise. We explore deterministic selection dynamics with and without mutation. Using different error rates and payoff values, we observe convergence to a small number of distinct equilibria. Two of them are uncooperative strict Nash equilibria representing always-defect (ALLD) and Grim. The third equilibrium is mixed and represents a cooperative alliance of several strategies, dominated by a strategy which we call Forgiver. Forgiver cooperates whenever the opponent has cooperated; it defects once when the opponent has defected, but subsequently Forgiver attempts to re-establish cooperation even if the opponent has defected again. Forgiver is not an evolutionarily stable strategy, but the alliance, which it rules, is asymptotically stable. For a wide range of parameter values the most commonly observed outcome is convergence to the mixed equilibrium, dominated by Forgiver. Our results show that although forgiving might incur a short-term loss it can lead to a long-term gain. Forgiveness facilitates stable cooperation in the presence of exploitation and noise.},
author = {Zagorsky, Benjamin and Reiter, Johannes and Chatterjee, Krishnendu and Nowak, Martin},
journal = {PLoS One},
number = {12},
publisher = {Public Library of Science},
title = {{Forgiver triumphs in alternating prisoner's dilemma }},
doi = {10.1371/journal.pone.0080814},
volume = {8},
year = {2013},
}
@inproceedings{2279,
abstract = {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.},
author = {Chatterjee, Krishnendu and Doyen, Laurent and Randour, Mickael and Raskin, Jean},
location = {Hanoi, Vietnam},
pages = {118 -- 132},
publisher = {Springer},
title = {{Looking at mean-payoff and total-payoff through windows}},
doi = {10.1007/978-3-319-02444-8_10},
volume = {8172},
year = {2013},
}
@proceedings{2292,
abstract = {This book constitutes the thoroughly refereed conference proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The 67 revised full papers presented together with six invited talks were carefully selected from 191 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence.},
editor = {Chatterjee, Krishnendu and Sgall, Jiri},
isbn = {978-3-642-40312-5},
location = {Klosterneuburg, Austria},
pages = {VI -- 854},
publisher = {Springer},
title = {{Mathematical Foundations of Computer Science 2013}},
doi = {10.1007/978-3-642-40313-2},
volume = {8087},
year = {2013},
}
@inproceedings{2295,
abstract = {We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. 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 known to be undecidable even for very special cases of parity objectives, we establish decidability (with optimal EXPTIME-complete complexity) of the qualitative analysis problems for POMDPs with all parity objectives under finite-memory strategies. We also establish asymptotically optimal (exponential) memory bounds.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Tracol, Mathieu},
location = {Torino, Italy},
pages = {165 -- 180},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{What is decidable about partially observable Markov decision processes with omega-regular objectives}},
doi = {10.4230/LIPIcs.CSL.2013.165},
volume = {23},
year = {2013},
}
@article{2299,
abstract = {The standard hardware design flow involves: (a) design of an integrated circuit using a hardware description language, (b) extensive functional and formal verification, and (c) logical synthesis. However, the above-mentioned processes consume significant effort and time. An alternative approach is to use a formal specification language as a high-level hardware description language and synthesize hardware from formal specifications. Our work is a case study of the synthesis of the widely and industrially used AMBA AHB protocol from formal specifications. Bloem et al. presented the first formal specifications for the AMBA AHB Arbiter and synthesized the AHB Arbiter circuit. However, in the first formal specification some important assumptions were missing. Our contributions are as follows: (a) We present detailed formal specifications for the AHB Arbiter incorporating the missing details, and obtain significant improvements in the synthesis results (both with respect to the number of gates in the synthesized circuit and with respect to the time taken to synthesize the circuit), and (b) we present formal specifications to generate compact circuits for the remaining two main components of AMBA AHB, namely, AHB Master and AHB Slave. Thus with systematic description we are able to automatically and completely synthesize an important and widely used industrial protocol.},
author = {Godhal, Yashdeep and Chatterjee, Krishnendu and Henzinger, Thomas A},
journal = {International Journal on Software Tools for Technology Transfer},
number = {5-6},
pages = {585 -- 601},
publisher = {Springer},
title = {{Synthesis of AMBA AHB from formal specification: A case study}},
doi = {10.1007/s10009-011-0207-9},
volume = {15},
year = {2013},
}
@inproceedings{2305,
abstract = {We study the complexity of central controller synthesis problems for finite-state Markov decision processes, where the objective is to optimize both the expected mean-payoff performance of the system and its stability. e argue that the basic theoretical notion of expressing the stability in terms of the variance of the mean-payoff (called global variance in our paper) is not always sufficient, since it ignores possible instabilities on respective runs. For this reason we propose alernative definitions of stability, which we call local and hybrid variance, and which express how rewards on each run deviate from the run's own mean-payoff and from the expected mean-payoff, respectively. We show that a strategy ensuring both the expected mean-payoff and the variance below given bounds requires randomization and memory, under all the above semantics of variance. We then look at the problem of determining whether there is a such a strategy. For the global variance, we show that the problem is in PSPACE, and that the answer can be approximated in pseudo-polynomial time. For the hybrid variance, the analogous decision problem is in NP, and a polynomial-time approximating algorithm also exists. For local variance, we show that the decision problem is in NP. Since the overall performance can be traded for stability (and vice versa), we also present algorithms for approximating the associated Pareto curve in all the three cases. Finally, we study a special case of the decision problems, where we require a given expected mean-payoff together with zero variance. Here we show that the problems can be all solved in polynomial time.},
author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Forejt, Vojtěch and Kučera, Antonín},
booktitle = {28th Annual ACM/IEEE Symposium},
location = {New Orleans, LA, United States},
pages = {331 -- 340},
publisher = {IEEE},
title = {{Trading performance for stability in Markov decision processes}},
doi = {10.1109/LICS.2013.39},
year = {2013},
}
@inproceedings{2329,
abstract = {Two-player games on graphs are central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work, we consider both finite-state game graphs, and recursive game graphs (or pushdown game graphs) that model the control flow of sequential programs with recursion. The objectives we study are multidimensional mean-payoff objectives, where the goal of player 1 is to ensure that the mean-payoff is non-negative in all dimensions. In pushdown games two types of strategies are relevant: (1) global strategies, that depend on the entire global history; and (2) modular strategies, that have only local memory and thus do not depend on the context of invocation. Our main contributions are as follows: (1) We show that finite-state multidimensional mean-payoff games can be solved in polynomial time if the number of dimensions and the maximal absolute value of the weights are fixed; whereas if the number of dimensions is arbitrary, then the problem is known to be coNP-complete. (2) We show that pushdown graphs with multidimensional mean-payoff objectives can be solved in polynomial time. For both (1) and (2) our algorithms are based on hyperplane separation technique. (3) For pushdown games under global strategies both one and multidimensional mean-payoff objectives problems are known to be undecidable, and we show that under modular strategies the multidimensional problem is also undecidable; under modular strategies the one-dimensional problem is NP-complete. We show that if the number of modules, the number of exits, and the maximal absolute value of the weights are fixed, then pushdown games under modular strategies with one-dimensional mean-payoff objectives can be solved in polynomial time, and if either the number of exits or the number of modules is unbounded, then the problem is NP-hard. (4) Finally we show that a fixed parameter tractable algorithm for finite-state multidimensional mean-payoff games or pushdown games under modular strategies with one-dimensional mean-payoff objectives would imply the fixed parameter tractability of parity games.},
author = {Chatterjee, Krishnendu and Velner, Yaron},
location = {Buenos Aires, Argentinia},
pages = {500 -- 515},
publisher = {Springer},
title = {{Hyperplane separation technique for multidimensional mean-payoff games}},
doi = {10.1007/978-3-642-40184-8_35},
volume = {8052},
year = {2013},
}
@inproceedings{2444,
abstract = {We consider two core algorithmic problems for probabilistic verification: the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs). For MDPs with treewidth k, we present two improved static algorithms for both the problems that run in time O(n·k 2.38·2k ) and O(m·logn· k), respectively, where n is the number of states and m is the number of edges, significantly improving the previous known O(n·k·√n· k) bound for low treewidth. We also present decremental algorithms for both problems for MDPs with constant treewidth that run in amortized logarithmic time, which is a huge improvement over the previously known algorithms that require amortized linear time.},
author = {Chatterjee, Krishnendu and Ła̧Cki, Jakub},
location = {St. Petersburg, Russia},
pages = {543 -- 558},
publisher = {Springer},
title = {{Faster algorithms for Markov decision processes with low treewidth}},
doi = {10.1007/978-3-642-39799-8_36},
volume = {8044},
year = {2013},
}
@inproceedings{2446,
abstract = {The model-checking problem for probabilistic systems crucially relies on the translation of LTL to deterministic Rabin automata (DRW). Our recent Safraless translation [KE12, GKE12] for the LTL(F,G) fragment produces smaller automata as compared to the traditional approach. In this work, instead of DRW we consider deterministic automata with acceptance condition given as disjunction of generalized Rabin pairs (DGRW). The Safraless translation of LTL(F,G) formulas to DGRW results in smaller automata as compared to DRW. We present algorithms for probabilistic model-checking as well as game solving for DGRW conditions. Our new algorithms lead to improvement both in terms of theoretical bounds as well as practical evaluation. We compare PRISM with and without our new translation, and show that the new translation leads to significant improvements.},
author = {Chatterjee, Krishnendu and Gaiser, Andreas and Kretinsky, Jan},
location = {St. Petersburg, Russia},
pages = {559 -- 575},
publisher = {Springer},
title = {{Automata with generalized Rabin pairs for probabilistic model checking and LTL synthesis}},
doi = {10.1007/978-3-642-39799-8_37},
volume = {8044},
year = {2013},
}
@misc{5399,
abstract = {In this work we present a flexible tool for tumor progression, which simulates the evolutionary dynamics of cancer. Tumor progression implements a multi-type branching process where the key parameters are the fitness landscape, the mutation rate, and the average time of cell division. The fitness of a cancer cell depends on the mutations it has accumulated. The input to our tool could be any fitness landscape, mutation rate, and cell division time, and the tool produces the growth dynamics and all relevant statistics.},
author = {Reiter, Johannes and Bozic, Ivana and Chatterjee, Krishnendu and Nowak, Martin},
issn = {2664-1690},
pages = {17},
publisher = {IST Austria},
title = {{TTP: Tool for Tumor Progression}},
doi = {10.15479/AT:IST-2013-104-v1-1},
year = {2013},
}
@misc{5400,
abstract = {We consider partially observable Markov decision processes (POMDPs) with ω-regular conditions specified as parity objectives. The class of ω-regular languages extends regular languages to infinite strings and provides a robust specification language to express all properties used in verification, and parity objectives are canonical forms to express ω-regular conditions. The qualitative analysis problem given a POMDP and a parity objective asks whether there is a strategy to ensure that the objective is satis- fied with probability 1 (resp. positive probability). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, we establish decidability (with optimal complexity) of the qualitative analysis problems for POMDPs with all parity objectives under finite- memory strategies. We establish asymptotically optimal (exponential) memory bounds and EXPTIME- completeness of the qualitative analysis problems under finite-memory strategies for POMDPs with parity objectives.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Tracol, Mathieu},
issn = {2664-1690},
pages = {41},
publisher = {IST Austria},
title = {{What is decidable about partially observable Markov decision processes with ω-regular objectives}},
doi = {10.15479/AT:IST-2013-109-v1-1},
year = {2013},
}
@misc{5403,
abstract = {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 every 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 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 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 mean-payoff games) that is not known to be in polynomial time.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus},
issn = {2664-1690},
pages = {33},
publisher = {IST Austria},
title = {{Qualitative analysis of concurrent mean-payoff games}},
doi = {10.15479/AT:IST-2013-126-v1-1},
year = {2013},
}