@article{2848,
abstract = {We study evolutionary game theory in a setting where individuals learn from each other. We extend the traditional approach by assuming that a population contains individuals with different learning abilities. In particular, we explore the situation where individuals have different search spaces, when attempting to learn the strategies of others. The search space of an individual specifies the set of strategies learnable by that individual. The search space is genetically given and does not change under social evolutionary dynamics. We introduce a general framework and study a specific example in the context of direct reciprocity. For this example, we obtain the counter intuitive result that cooperation can only evolve for intermediate benefit-to-cost ratios, while small and large benefit-to-cost ratios favor defection. Our paper is a step toward making a connection between computational learning theory and evolutionary game dynamics.},
author = {Chatterjee, Krishnendu and Zufferey, Damien and Nowak, Martin},
journal = {Journal of Theoretical Biology},
pages = {161 -- 173},
publisher = {Elsevier},
title = {{Evolutionary game dynamics in populations with different learners}},
doi = {10.1016/j.jtbi.2012.02.021},
volume = {301},
year = {2012},
}
@inproceedings{2916,
abstract = {The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a quantitative measure for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intu- itively, 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, and that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces. 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},
booktitle = {Electronic Proceedings in Theoretical Computer Science},
location = {Napoli, Italy},
pages = {29 -- 42},
publisher = {EPTCS},
title = {{Interface Simulation Distances}},
doi = {10.4204/EPTCS.96.3},
volume = {96},
year = {2012},
}
@inproceedings{2936,
abstract = {The notion of delays arises naturally in many computational models, such as, in the design of circuits, control systems, and dataflow languages. In this work, we introduce automata with delay blocks (ADBs), extending finite state automata with variable time delay blocks, for deferring individual transition output symbols, in a discrete-time setting. We show that the ADB languages strictly subsume the regular languages, and are incomparable in expressive power to the context-free languages. We show that ADBs are closed under union, concatenation and Kleene star, and under intersection with regular languages, but not closed under complementation and intersection with other ADB languages. We show that the emptiness and the membership problems are decidable in polynomial time for ADBs, whereas the universality problem is undecidable. Finally we consider the linear-time model checking problem, i.e., whether the language of an ADB is contained in a regular language, and show that the model checking problem is PSPACE-complete. Copyright 2012 ACM.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Prabhu, Vinayak},
booktitle = {roceedings of the tenth ACM international conference on Embedded software},
location = {Tampere, Finland},
pages = {43 -- 52},
publisher = {ACM},
title = {{Finite automata with time delay blocks}},
doi = {10.1145/2380356.2380370},
year = {2012},
}
@inproceedings{2947,
abstract = {We introduce games with probabilistic uncertainty, a model for controller synthesis in which the controller observes the state through imprecise sensors that provide correct information about the current state with a fixed probability. That is, in each step, the sensors return an observed state, and given the observed state, there is a probability distribution (due to the estimation error) over the actual current state. The controller must base its decision on the observed state (rather than the actual current state, which it does not know). On the other hand, we assume that the environment can perfectly observe the current state. We show that controller synthesis for qualitative ω-regular objectives in our model can be reduced in polynomial time to standard partial-observation stochastic games, and vice-versa. As a consequence we establish the precise decidability frontier for the new class of games, and establish optimal complexity results for all the decidable problems.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Majumdar, Ritankar},
location = {Thiruvananthapuram, India},
pages = {385 -- 399},
publisher = {Springer},
title = {{Equivalence of games with probabilistic uncertainty and partial observation games}},
doi = {10.1007/978-3-642-33386-6_30},
volume = {7561},
year = {2012},
}
@inproceedings{2955,
abstract = {We consider two-player stochastic games played on finite graphs with 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 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, the players (a) may not be allowed to use randomization (pure strategies), or (b) may choose a probability distribution over actions but the actual random choice is external and not visible to the player (actions invisible), or (c) may use full randomization. Our main results for pure strategies are as follows. (1) For one-sided games with player 1 having partial 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 almostsure 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. (2) For one-sided games with player 2 having partial observation we show that non-elementary memory 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 non-elementary 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 exhibits serious flaws in previous results of the literature: we show a non-elementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
booktitle = {Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science},
location = {Dubrovnik, Croatia},
publisher = {IEEE},
title = {{Partial-observation stochastic games: How to win when belief fails}},
doi = {10.1109/LICS.2012.28},
year = {2012},
}
@inproceedings{2956,
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 solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion. While pushdown games have been studied before with qualitative objectives, such as reachability and parity objectives, in this work we study for the first time such games with the most well-studied quantitative objective, namely, mean payoff objectives. 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, but only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two-player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP-hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games; and memoryless modular strategies are sufficient in two-player pushdown games. Finally we also show that all the problems have the same computational complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.},
author = {Chatterjee, Krishnendu and Velner, Yaron},
booktitle = {Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science},
location = {Dubrovnik, Croatia },
publisher = {IEEE},
title = {{Mean payoff pushdown games}},
doi = {10.1109/LICS.2012.30},
year = {2012},
}
@inproceedings{2957,
abstract = {We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with positive probability; (ii) the almost decision problem asks whether there is a word that is accepted with probability 1; and (iii) the limit decision problem asks whether words are accepted with probability arbitrarily close to 1. We unify and generalize several decidability results for probabilistic automata over infinite words, and identify a robust (closed under union and intersection) subclass of probabilistic automata for which all the qualitative decision problems are decidable for parity conditions. We also show that if the input words are restricted to lasso shape (regular) words, then the positive and almost problems are decidable for all probabilistic automata with parity conditions. For most decidable problems we show an optimal PSPACE-complete complexity bound.},
author = {Chatterjee, Krishnendu and Tracol, Mathieu},
booktitle = {Proceedings of the 2012 27th Annual ACM/IEEE Symposium on Logic in Computer Science},
location = {Dubrovnik, Croatia },
publisher = {IEEE},
title = {{Decidable problems for probabilistic automata on infinite words}},
doi = {10.1109/LICS.2012.29},
year = {2012},
}
@article{2972,
abstract = {Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of energy in the game) must remain positive. Beside their own interest in the design and synthesis of resource-constrained omega-regular specifications, energy parity games provide one of the simplest model of games with combined qualitative and quantitative objectives. Our main results are as follows: (a) exponential memory is sufficient and may be necessary for winning strategies in energy parity games; (b) the problem of deciding the winner in energy parity games can be solved in NP ∩ coNP; and (c) we give an algorithm to solve energy parity by reduction to energy games. We also show that the problem of deciding the winner in energy parity games is logspace-equivalent to the problem of deciding the winner in mean-payoff parity games, which can thus be solved in NP ∩ coNP. As a consequence we also obtain a conceptually simple algorithm to solve mean-payoff parity games.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
journal = {Theoretical Computer Science},
pages = {49 -- 60},
publisher = {Elsevier},
title = {{Energy parity games}},
doi = {10.1016/j.tcs.2012.07.038},
volume = {458},
year = {2012},
}
@inproceedings{495,
abstract = {An automaton with advice is a finite state automaton which has access to an additional fixed infinite string called an advice tape. We refine the Myhill-Nerode theorem to characterize the languages of finite strings that are accepted by automata with advice. We do the same for tree automata with advice.},
author = {Kruckman, Alex and Rubin, Sasha and Sheridan, John and Zax, Ben},
booktitle = {Proceedings GandALF 2012},
location = {Napoli, Italy},
pages = {238 -- 246},
publisher = {Open Publishing Association},
title = {{A Myhill Nerode theorem for automata with advice}},
doi = {10.4204/EPTCS.96.18},
volume = {96},
year = {2012},
}
@inproceedings{496,
abstract = {We study the expressive power of logical interpretations on the class of scattered trees, namely those with countably many infinite branches. Scattered trees can be thought of as the tree analogue of scattered linear orders. Every scattered tree has an ordinal rank that reflects the structure of its infinite branches. We prove, roughly, that trees and orders of large rank cannot be interpreted in scattered trees of small rank. We consider a quite general notion of interpretation: each element of the interpreted structure is represented by a set of tuples of subsets of the interpreting tree. Our trees are countable, not necessarily finitely branching, and may have finitely many unary predicates as labellings. We also show how to replace injective set-interpretations in (not necessarily scattered) trees by 'finitary' set-interpretations.},
author = {Rabinovich, Alexander and Rubin, Sasha},
location = {Dubrovnik, Croatia},
publisher = {IEEE},
title = {{Interpretations in trees with countably many branches}},
doi = {10.1109/LICS.2012.65},
year = {2012},
}
@inproceedings{497,
abstract = {One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the notion of simulation. Alternating transition systems (ATSs) provide a general model for composite reactive systems, and the simulation relation for ATSs is known as alternating simulation. The simulation relation for fair transition systems is called fair simulation. In this work our main contributions are as follows: (1) We present an improved algorithm for fair simulation with Büchi fairness constraints; our algorithm requires O(n 3·m) time as compared to the previous known O(n 6)-time algorithm, where n is the number of states and m is the number of transitions. (2) We present a game based algorithm for alternating simulation that requires O(m2)-time as compared to the previous known O((n·m)2)-time algorithm, where n is the number of states and m is the size of transition relation. (3) We present an iterative algorithm for alternating simulation that matches the time complexity of the game based algorithm, but is more space efficient than the game based algorithm. © Krishnendu Chatterjee, Siddhesh Chaubal, and Pritish Kamath.},
author = {Chatterjee, Krishnendu and Chaubal, Siddhesh and Kamath, Pritish},
location = {Fontainebleau, France},
pages = {167 -- 182},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Faster algorithms for alternating refinement relations}},
doi = {10.4230/LIPIcs.CSL.2012.167},
volume = {16},
year = {2012},
}
@misc{5377,
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 solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion. While pushdown games have been studied before with qualitative objectives, such as reachability and ω-regular objectives, in this work we study for the first time such games with the most well-studied quantitative objective, namely, mean-payoff objectives. 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, but only on the history of the current invocation of the module. Our main results are as follows: (1) One-player pushdown games with mean-payoff objectives under global strategies are decidable in polynomial time. (2) Two- player pushdown games with mean-payoff objectives under global strategies are undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies are NP- hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies are NP-complete). We also establish the optimal strategy complexity showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games; and memoryless modular strategies are sufficient in two- player pushdown games. Finally we also show that all the problems have the same complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.},
author = {Chatterjee, Krishnendu and Velner, Yaron},
issn = {2664-1690},
pages = {33},
publisher = {IST Austria},
title = {{Mean-payoff pushdown games}},
doi = {10.15479/AT:IST-2012-0002},
year = {2012},
}
@misc{5378,
abstract = {One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the notion of simulation. Alternating transition systems (ATSs) provide a general model for composite reactive systems, and the simulation relation for ATSs is known as alternating simulation. The simulation relation for fair transition systems is called fair simulation. In this work our main contributions are as follows: (1) We present an improved algorithm for fair simulation with Büchi fairness constraints; our algorithm requires O(n3 · m) time as compared to the previous known O(n6)-time algorithm, where n is the number of states and m is the number of transitions. (2) We present a game based algorithm for alternating simulation that requires O(m2)-time as compared to the previous known O((n · m)2)-time algorithm, where n is the number of states and m is the size of transition relation. (3) We present an iterative algorithm for alternating simulation that matches the time complexity of the game based algorithm, but is more space efficient than the game based algorithm.},
author = {Chatterjee, Krishnendu and Chaubal, Siddhesh and Kamath, Pritish},
issn = {2664-1690},
pages = {21},
publisher = {IST Austria},
title = {{Faster algorithms for alternating refinement relations}},
doi = {10.15479/AT:IST-2012-0001},
year = {2012},
}
@article{3846,
abstract = {We summarize classical and recent results about two-player games played on graphs with ω-regular objectives. These games have applications in the verification and synthesis of reactive systems. Important distinctions are whether a graph game is turn-based or concurrent; deterministic or stochastic; zero-sum or not. We cluster known results and open problems according to these classifications.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A},
journal = {Journal of Computer and System Sciences},
number = {2},
pages = {394 -- 413},
publisher = {Elsevier},
title = {{A survey of stochastic ω regular games}},
doi = {10.1016/j.jcss.2011.05.002},
volume = {78},
year = {2012},
}
@article{3128,
abstract = {We consider two-player zero-sum stochastic games on graphs with ω-regular winning conditions specified as parity objectives. These games have applications in the design and control of reactive systems. We survey the complexity results for the problem of deciding the winner in such games, and in classes of interest obtained as special cases, based on the information and the power of randomization available to the players, on the class of objectives and on the winning mode. On the basis of information, these games can be classified as follows: (a) 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) complete-observation (both players have complete view of the game). The one-sided partial-observation games have two important subclasses: the one-player games, known as partial-observation Markov decision processes (POMDPs), and the blind one-player games, known as probabilistic automata. 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. Finally, various classes of games are obtained by restricting the parity objective to a reachability, safety, Büchi, or coBüchi condition. We also consider several winning modes, such as sure-winning (i.e., all outcomes of a strategy have to satisfy the winning condition), almost-sure winning (i.e., winning with probability 1), limit-sure winning (i.e., winning with probability arbitrarily close to 1), and value-threshold winning (i.e., winning with probability at least ν, where ν is a given rational). },
author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A},
journal = {Formal Methods in System Design},
number = {2},
pages = {268 -- 284},
publisher = {Springer},
title = {{A survey of partial-observation stochastic parity games}},
doi = {10.1007/s10703-012-0164-2},
volume = {43},
year = {2012},
}
@inproceedings{3135,
abstract = {We introduce consumption games, a model for discrete interactive system with multiple resources that are consumed or reloaded independently. More precisely, a consumption game is a finite-state graph where each transition is labeled by a vector of resource updates, where every update is a non-positive number or ω. The ω updates model the reloading of a given resource. Each vertex belongs either to player □ or player ◇, where the aim of player □ is to play so that the resources are never exhausted. We consider several natural algorithmic problems about consumption games, and show that although these problems are computationally hard in general, they are solvable in polynomial time for every fixed number of resource types (i.e., the dimension of the update vectors) and bounded resource updates. },
author = {Brázdil, Brázdil and Chatterjee, Krishnendu and Kučera, Antonín and Novotny, Petr},
location = {Berkeley, CA, USA},
pages = {23 -- 38},
publisher = {Springer},
title = {{Efficient controller synthesis for consumption games with multiple resource types}},
doi = {10.1007/978-3-642-31424-7_8},
volume = {7358},
year = {2012},
}
@article{3157,
abstract = {Colorectal tumours that are wild type for KRAS are often sensitive to EGFR blockade, but almost always develop resistance within several months of initiating therapy. The mechanisms underlying this acquired resistance to anti-EGFR antibodies are largely unknown. This situation is in marked contrast to that of small-molecule targeted agents, such as inhibitors of ABL, EGFR, BRAF and MEK, in which mutations in the genes encoding the protein targets render the tumours resistant to the effects of the drugs. The simplest hypothesis to account for the development of resistance to EGFR blockade is that rare cells with KRAS mutations pre-exist at low levels in tumours with ostensibly wild-type KRAS genes. Although this hypothesis would seem readily testable, there is no evidence in pre-clinical models to support it, nor is there data from patients. To test this hypothesis, we determined whether mutant KRAS DNA could be detected in the circulation of 28 patients receiving monotherapy with panitumumab, a therapeutic anti-EGFR antibody. We found that 9 out of 24 (38%) patients whose tumours were initially KRAS wild type developed detectable mutations in KRAS in their sera, three of which developed multiple different KRAS mutations. The appearance of these mutations was very consistent, generally occurring between 5 and 6months following treatment. Mathematical modelling indicated that the mutations were present in expanded subclones before the initiation of panitumumab treatment. These results suggest that the emergence of KRAS mutations is a mediator of acquired resistance to EGFR blockade and that these mutations can be detected in a non-invasive manner. They explain why solid tumours develop resistance to targeted therapies in a highly reproducible fashion.},
author = {Diaz Jr, Luis and Williams, Richard and Wu, Jian and Kinde, Isaac and Hecht, Joel and Berlin, Jordan and Allen, Benjamin and Božić, Ivana and Reiter, Johannes and Nowak, Martin and Kinzler, Kenneth and Oliner, Kelly and Vogelstein, Bert},
journal = {Nature},
number = {7404},
pages = {537 -- 540},
publisher = {Nature Publishing Group},
title = {{The molecular evolution of acquired resistance to targeted EGFR blockade in colorectal cancers}},
doi = {10.1038/nature11219},
volume = {486},
year = {2012},
}
@inproceedings{3165,
abstract = {Computing 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(n 2). This bound also leads to O(n 2) 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(n 3)), and (3) in Markov decision processes (improving for m > n 4/3 an earlier bound of O(min(m 1.5, m·n 2/3)). We also show that the same technique can be used to compute the maximal end-component decomposition of a graph in time O(n 2), which is an improvement over earlier bounds for m > n 4/3. Finally, we 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. This is the first dynamic algorithm for this problem.},
author = {Chatterjee, Krishnendu and Henzinger, Monika},
booktitle = {Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms},
location = {Kyoto, Japan},
pages = {1386 -- 1399},
publisher = {SIAM},
title = {{An O(n2) time algorithm for alternating Büchi games}},
doi = {10.1137/1.9781611973099.109},
year = {2012},
}
@inproceedings{3252,
abstract = {We study the automatic synthesis of fair non-repudiation protocols, a class of fair exchange protocols, used for digital contract signing. First, we show how to specify the objectives of the participating agents, the trusted third party (TTP) and the protocols as path formulas in Linear Temporal Logic (LTL) and prove that the satisfaction of the objectives of the agents and the TTP imply satisfaction of the protocol objectives. We then show that weak (co-operative) co-synthesis and classical (strictly competitive) co-synthesis fail in synthesizing these protocols, whereas assume-guarantee synthesis (AGS) succeeds. We demonstrate the success of assume-guarantee synthesis as follows: (a) any solution of assume-guarantee synthesis is attack-free; no subset of participants can violate the objectives of the other participants without violating their own objectives; (b) the Asokan-Shoup-Waidner (ASW) certified mail protocol that has known vulnerabilities is not a solution of AGS; and (c) the Kremer-Markowitch (KM) non-repudiation protocol is a solution of AGS. To our knowledge this is the first application of synthesis to fair non-repudiation protocols, and our results show how synthesis can generate correct protocols and automatically discover vulnerabilities. The solution to assume-guarantee synthesis can be computed efficiently as the secure equilibrium solution of three-player graph games. © 2012 Springer-Verlag.},
author = {Chatterjee, Krishnendu and Raman, Vishwanath},
location = {Philadelphia, PA, USA},
pages = {152 -- 168},
publisher = {Springer},
title = {{Synthesizing protocols for digital contract signing}},
doi = {10.1007/978-3-642-27940-9_11},
volume = {7148},
year = {2012},
}
@article{3254,
abstract = {The theory of graph games with ω-regular winning conditions is the foundation for modeling and synthesizing reactive processes. In the case of stochastic reactive processes, the corresponding stochastic graph games have three players, two of them (System and Environment) behaving adversarially, and the third (Uncertainty) behaving probabilistically. We consider two problems for stochastic graph games: the qualitative problem asks for the set of states from which a player can win with probability 1 (almost-sure winning); and the quantitative problem asks for the maximal probability of winning (optimal winning) from each state. We consider ω-regular winning conditions formalized as Müller winning conditions. We present optimal memory bounds for pure (deterministic) almost-sure winning and optimal winning strategies in stochastic graph games with Müller winning conditions. We also study the complexity of stochastic Müller games and show that both the qualitative and quantitative analysis problems are PSPACE-complete. Our results are relevant in synthesis of stochastic reactive processes.},
author = {Chatterjee, Krishnendu},
journal = {Information and Computation},
pages = {29 -- 48},
publisher = {Elsevier},
title = {{The complexity of stochastic Müller games}},
doi = {10.1016/j.ic.2011.11.004},
volume = {211},
year = {2012},
}
@inproceedings{3255,
abstract = {In this paper we survey results of two-player games on graphs and Markov decision processes with parity, mean-payoff and energy objectives, and the combination of mean-payoff and energy objectives with parity objectives. These problems have applications in verification and synthesis of reactive systems in resource-constrained environments.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
location = {Lednice, Czech Republic},
pages = {37 -- 46},
publisher = {Springer},
title = {{Games and Markov decision processes with mean payoff parity and energy parity objectives}},
doi = {10.1007/978-3-642-25929-6_3},
volume = {7119},
year = {2012},
}
@article{3260,
abstract = {Many scenarios in the living world, where individual organisms compete for winning positions (or resources), have properties of auctions. Here we study the evolution of bids in biological auctions. For each auction, n individuals are drawn at random from a population of size N. Each individual makes a bid which entails a cost. The winner obtains a benefit of a certain value. Costs and benefits are translated into reproductive success (fitness). Therefore, successful bidding strategies spread in the population. We compare two types of auctions. In “biological all-pay auctions”, the costs are the bid for every participating individual. In “biological second price all-pay auctions”, the cost for everyone other than the winner is the bid, but the cost for the winner is the second highest bid. Second price all-pay auctions are generalizations of the “war of attrition” introduced by Maynard Smith. We study evolutionary dynamics in both types of auctions. We calculate pairwise invasion plots and evolutionarily stable distributions over the continuous strategy space. We find that the average bid in second price all-pay auctions is higher than in all-pay auctions, but the average cost for the winner is similar in both auctions. In both cases, the average bid is a declining function of the number of participants, n. The more individuals participate in an auction the smaller is the chance of winning, and thus expensive bids must be avoided.
},
author = {Chatterjee, Krishnendu and Reiter, Johannes and Nowak, Martin},
journal = {Theoretical Population Biology},
number = {1},
pages = {69 -- 80},
publisher = {Academic Press},
title = {{Evolutionary dynamics of biological auctions}},
doi = {10.1016/j.tpb.2011.11.003},
volume = {81},
year = {2012},
}
@article{3314,
abstract = {We introduce two-level discounted and mean-payoff games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted or mean-payoff game and the lower level game is a (undiscounted) reachability game. Two-level games model hierarchical and sequential decision making under uncertainty across different time scales. For both discounted and mean-payoff two-level games, we show the existence of pure memoryless optimal strategies for both players and an ordered field property. We show that if there is only one player (Markov decision processes), then the values can be computed in polynomial time. It follows that whether the value of a player is equal to a given rational constant in two-level discounted or mean-payoff games can be decided in NP ∩ coNP. We also give an alternate strategy improvement algorithm to compute the value. © 2012 World Scientific Publishing Company.},
author = {Chatterjee, Krishnendu and Majumdar, Ritankar},
journal = {International Journal of Foundations of Computer Science},
number = {3},
pages = {609 -- 625},
publisher = {World Scientific Publishing},
title = {{Discounting and averaging in games across time scales}},
doi = {10.1142/S0129054112400308},
volume = {23},
year = {2012},
}
@inproceedings{3341,
abstract = {We consider two-player stochastic games played on a finite state space for an infinite number of rounds. The games are concurrent: 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 a probability distribution over the successor states. We also consider the important special case of turn-based stochastic games where players make moves in turns, rather than concurrently. We study concurrent games with \omega-regular winning conditions specified as parity objectives. The value for player 1 for a parity objective is the maximal probability with which the player can guarantee the satisfaction of the objective against all strategies of the opponent. We study the problem of continuity and robustness of the value function in concurrent and turn-based stochastic parity gameswith respect to imprecision in the transition probabilities. We present quantitative bounds on the difference of the value function (in terms of the imprecision of the transition probabilities) and show the value continuity for structurally equivalent concurrent games (two games are structurally equivalent if the support of the transition function is same and the probabilities differ). We also show robustness of optimal strategies for structurally equivalent turn-based stochastic parity games. Finally we show that the value continuity property breaks without the structurally equivalent assumption (even for Markov chains) and show that our quantitative bound is asymptotically optimal. Hence our results are tight (the assumption is both necessary and sufficient) and optimal (our quantitative bound is asymptotically optimal).},
author = {Chatterjee, Krishnendu},
location = {Tallinn, Estonia},
pages = {270 -- 285},
publisher = {Springer},
title = {{Robustness of structurally equivalent concurrent parity games}},
doi = {10.1007/978-3-642-28729-9_18},
volume = {7213},
year = {2012},
}
@misc{5379,
abstract = {Computing 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 ̃O(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 ̃O(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 O(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(min(m1.5, m·n2/3)). We also show that the same technique can be used to compute the maximal end-component decomposition of a graph in time O(n2), which is an improvement over earlier bounds for m > n4/3. Finally, we 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. This is the first dynamic algorithm for this problem.},
author = {Chatterjee, Krishnendu and Henzinger, Monika},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{An O(n2) time algorithm for alternating Büchi games}},
doi = {10.15479/AT:IST-2011-0009},
year = {2011},
}
@misc{5380,
abstract = {We consider 2-player games played on a finite state space for an infinite number of rounds. The games are concurrent: 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. We study concurrent games with 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). 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 O(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. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms,that are obtained by characterization of the winning sets as μ-calculus formulas, are considerably more involved than those for turn-based games.},
author = {Chatterjee, Krishnendu},
issn = {2664-1690},
pages = {53},
publisher = {IST Austria},
title = {{Bounded rationality in concurrent parity games}},
doi = {10.15479/AT:IST-2011-0008},
year = {2011},
}
@misc{5381,
abstract = {In two-player finite-state stochastic games of partial obser- vation on graphs, in every state of the graph, the players simultaneously choose an action, and their joint actions determine a probability distri- bution 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 pos- itively (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 perfect observation we show that (in contrast to full randomized strategies) belief-based (subset-construction based) strate- gies are not sufficient, and present an exponential upper bound on mem- ory 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 algo- rithms that avoid the explicit exponential construction. (2) For one-sided games with player 1 perfect observation we show that non-elementary memory is both necessary and sufficient for both almost-sure and posi- tive 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 non-elementary 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 re- sult exhibit serious flaws in previous results in the literature: we show a non-elementary memory lower bound for almost-sure winning whereas an exponential upper bound was previously claimed.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
issn = {2664-1690},
pages = {43},
publisher = {IST Austria},
title = {{Partial-observation stochastic games: How to win when belief fails}},
doi = {10.15479/AT:IST-2011-0007},
year = {2011},
}
@misc{5382,
abstract = {We consider two-player stochastic games played on a finite state space for an infinite num- ber of rounds. The games are concurrent: 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 a probability distribution over the successor states. We also consider the important special case of turn-based stochastic games where players make moves in turns, rather than concurrently. We study concurrent games with ω-regular winning conditions specified as parity objectives. The value for player 1 for a parity objective is the maximal probability with which the player can guarantee the satisfaction of the objective against all strategies of the opponent. We study the problem of continuity and robustness of the value function in concurrent and turn-based stochastic parity games with respect to imprecision in the transition probabilities. We present quantitative bounds on the difference of the value function (in terms of the imprecision of the transition probabilities) and show the value continuity for structurally equivalent concurrent games (two games are structurally equivalent if the support of the transition func- tion is same and the probabilities differ). We also show robustness of optimal strategies for structurally equivalent turn-based stochastic parity games. Finally we show that the value continuity property breaks without the structurally equivalent assumption (even for Markov chains) and show that our quantitative bound is asymptotically optimal. Hence our results are tight (the assumption is both necessary and sufficient) and optimal (our quantitative bound is asymptotically optimal).},
author = {Chatterjee, Krishnendu},
issn = {2664-1690},
pages = {18},
publisher = {IST Austria},
title = {{Robustness of structurally equivalent concurrent parity games}},
doi = {10.15479/AT:IST-2011-0006},
year = {2011},
}
@misc{5384,
abstract = {We consider probabilistic automata on infinite words with acceptance defined by parity conditions. We consider three qualitative decision problems: (i) the positive decision problem asks whether there is a word that is accepted with positive probability; (ii) the almost decision problem asks whether there is a word that is accepted with probability 1; and (iii) the limit decision problem asks whether for every ε > 0 there is a word that is accepted with probability at least 1 − ε. We unify and generalize several decidability results for probabilistic automata over infinite words, and identify a robust (closed under union and intersection) subclass of probabilistic automata for which all the qualitative decision problems are decidable for parity conditions. We also show that if the input words are restricted to lasso shape words, then the positive and almost problems are decidable for all probabilistic automata with parity conditions.},
author = {Chatterjee, Krishnendu and Tracol, Mathieu},
issn = {2664-1690},
pages = {30},
publisher = {IST Austria},
title = {{Decidable problems for probabilistic automata on infinite words}},
doi = {10.15479/AT:IST-2011-0004},
year = {2011},
}
@misc{5385,
abstract = {There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with “controlled-accumulation”, allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.},
author = {Boker, Udi and Chatterjee, Krishnendu and Henzinger, Thomas A and Kupferman, Orna},
issn = {2664-1690},
pages = {14},
publisher = {IST Austria},
title = {{Temporal specifications with accumulative values}},
doi = {10.15479/AT:IST-2011-0003},
year = {2011},
}
@misc{5387,
abstract = {We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean- payoff parity MDPs, the problem is solvable in polynomial time, improving a recent PSPACE bound.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{Energy and mean-payoff parity Markov decision processes}},
doi = {10.15479/AT:IST-2011-0001},
year = {2011},
}
@article{3315,
abstract = {We consider two-player games played in real time on game structures with clocks where the objectives of players are described using parity conditions. The games are concurrent in that at each turn, both players independently propose a time delay and an action, and the action with the shorter delay is chosen. To prevent a player from winning by blocking time, we restrict each player to play strategies that ensure that the player cannot be responsible for causing a zeno run. First, we present an efficient reduction of these games to turn-based (i.e., not concurrent) finite-state (i.e., untimed) parity games. Our reduction improves the best known complexity for solving timed parity games. Moreover, the rich class of algorithms for classical parity games can now be applied to timed parity games. The states of the resulting game are based on clock regions of the original game, and the state space of the finite game is linear in the size of the region graph. Second, we consider two restricted classes of strategies for the player that represents the controller in a real-time synthesis problem, namely, limit-robust and bounded-robust winning strategies. Using a limit-robust winning strategy, the controller cannot choose an exact real-valued time delay but must allow for some nonzero jitter in each of its actions. If there is a given lower bound on the jitter, then the strategy is bounded-robust winning. We show that exact strategies are more powerful than limit-robust strategies, which are more powerful than bounded-robust winning strategies for any bound. For both kinds of robust strategies, we present efficient reductions to standard timed automaton games. These reductions provide algorithms for the synthesis of robust real-time controllers.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Prabhu, Vinayak},
journal = {Logical Methods in Computer Science},
number = {4},
publisher = {International Federation of Computational Logic},
title = {{Timed parity games: Complexity and robustness}},
doi = {10.2168/LMCS-7(4:8)2011},
volume = {7},
year = {2011},
}
@inproceedings{3316,
abstract = {In addition to being correct, a system should be robust, that is, it should behave reasonably even after receiving unexpected inputs. In this paper, we summarize two formal notions of robustness that we have introduced previously for reactive systems. One of the notions is based on assigning costs for failures on a user-provided notion of incorrect transitions in a specification. Here, we define a system to be robust if a finite number of incorrect inputs does not lead to an infinite number of incorrect outputs. We also give a more refined notion of robustness that aims to minimize the ratio of output failures to input failures. The second notion is aimed at liveness. In contrast to the previous notion, it has no concept of recovery from an error. Instead, it compares the ratio of the number of liveness constraints that the system violates to the number of liveness constraints that the environment violates.},
author = {Bloem, Roderick and Chatterjee, Krishnendu and Greimel, Karin and Henzinger, Thomas A and Jobstmann, Barbara},
booktitle = {6th IEEE International Symposium on Industrial and Embedded Systems},
location = {Vasteras, Sweden},
pages = {176 -- 185},
publisher = {IEEE},
title = {{Specification-centered robustness}},
doi = {10.1109/SIES.2011.5953660},
year = {2011},
}
@unpublished{3338,
abstract = {We consider 2-player games played on a finite state space for an infinite number of rounds. The games are concurrent: in each round, the two players (player 1 and player 2) choose their moves inde- pendently and simultaneously; the current state and the two moves determine the successor state. We study concurrent games with 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, respec- tively. In general the almost-sure and limit-sure winning strategies require both infinite-memory as well as infinite-precision (to describe probabilities). 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 power- ful as infinite-precision finite-memory strategies. We show that the winning sets can be computed in O(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. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms, that are obtained by characterization of the winning sets as μ-calculus formulas, are considerably more involved than those for turn-based games.},
author = {Chatterjee, Krishnendu},
booktitle = {arXiv},
pages = {1 -- 51},
publisher = {ArXiv},
title = {{Bounded rationality in concurrent parity games}},
year = {2011},
}
@unpublished{3339,
abstract = {Turn-based stochastic games and its important subclass Markov decision processes (MDPs) provide models for systems with both probabilistic and nondeterministic behaviors. We consider turn-based stochastic games with two classical quantitative objectives: discounted-sum and long-run average objectives. The game models and the quantitative objectives are widely used in probabilistic verification, planning, optimal inventory control, network protocol and performance analysis. Games and MDPs that model realistic systems often have very large state spaces, and probabilistic abstraction techniques are necessary to handle the state-space explosion. The commonly used full-abstraction techniques do not yield space-savings for systems that have many states with similar value, but does not necessarily have similar transition structure. A semi-abstraction technique, namely Magnifying-lens abstractions (MLA), that clusters states based on value only, disregarding differences in their transition relation was proposed for qualitative objectives (reachability and safety objectives). In this paper we extend the MLA technique to solve stochastic games with discounted-sum and long-run average objectives. We present the MLA technique based abstraction-refinement algorithm for stochastic games and MDPs with discounted-sum objectives. For long-run average objectives, our solution works for all MDPs and a sub-class of stochastic games where every state has the same value. },
author = {Chatterjee, Krishnendu and De Alfaro, Luca and Pritam, Roy},
booktitle = {arXiv},
pages = {17},
publisher = {ArXiv},
title = {{Magnifying lens abstraction for stochastic games with discounted and long-run average objectives}},
year = {2011},
}
@inproceedings{3342,
abstract = {We consider Markov decision processes (MDPs) with ω-regular specifications given as parity objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. The algorithms for the computation of the almost-sure winning set for parity objectives iteratively use the solutions for the almost-sure winning set for Büchi objectives (a special case of parity objectives). Our contributions are as follows: First, we present the first subquadratic symbolic algorithm to compute the almost-sure winning set for MDPs with Büchi objectives; our algorithm takes O(nm) symbolic steps as compared to the previous known algorithm that takes O(n 2) symbolic steps, where n is the number of states and m is the number of edges of the MDP. In practice MDPs often have constant out-degree, and then our symbolic algorithm takes O(nn) symbolic steps, as compared to the previous known O(n 2) symbolic steps algorithm. Second, we present a new algorithm, namely win-lose algorithm, with the following two properties: (a) the algorithm iteratively computes subsets of the almost-sure winning set and its complement, as compared to all previous algorithms that discover the almost-sure winning set upon termination; and (b) requires O(nK) symbolic steps, where K is the maximal number of edges of strongly connected components (scc’s) of the MDP. The win-lose algorithm requires symbolic computation of scc’s. Third, we improve the algorithm for symbolic scc computation; the previous known algorithm takes linear symbolic steps, and our new algorithm improves the constants associated with the linear number of steps. In the worst case the previous known algorithm takes 5·n symbolic steps, whereas our new algorithm takes 4 ·n symbolic steps.},
author = {Chatterjee, Krishnendu and Henzinger, Monika and Joglekar, Manas and Nisarg, Shah},
editor = {Gopalakrishnan, Ganesh and Qadeer, Shaz},
location = {Snowbird, USA},
pages = {260 -- 276},
publisher = {Springer},
title = {{Symbolic algorithms for qualitative analysis of Markov decision processes with Büchi objectives}},
doi = {10.1007/978-3-642-22110-1_21},
volume = {6806},
year = {2011},
}
@inproceedings{3343,
abstract = {We present faster and dynamic algorithms for the following problems arising in probabilistic verification: Computation of the maximal end-component (mec) decomposition of Markov decision processes (MDPs), and of the almost sure winning set for reachability and parity objectives in MDPs. We achieve the following running time for static algorithms in MDPs with graphs of n vertices and m edges: (1) O(m · min{ √m, n2/3 }) for the mec decomposition, improving the longstanding O(m·n) bound; (2) O(m·n2/3) for reachability objectives, improving the previous O(m · √m) bound for m > n4/3; and (3) O(m · min{ √m, n2/3 } · log(d)) for parity objectives with d priorities, improving the previous O(m · √m · d) bound. We also give incremental and decremental algorithms in linear time for mec decomposition and reachability objectives and O(m · log d) time for parity ob jectives.},
author = {Chatterjee, Krishnendu and Henzinger, Monika},
location = {San Francisco, USA},
pages = {1318 -- 1336},
publisher = {SIAM},
title = {{Faster and dynamic algorithms for maximal end component decomposition and related graph problems in probabilistic verification}},
doi = {10.1137/1.9781611973082.101},
year = {2011},
}
@inproceedings{3344,
abstract = {Games played on graphs provide the mathematical framework to analyze several important problems in computer science as well as mathematics, such as the synthesis problem of Church, model checking of open reactive systems and many others. On the basis of mode of interaction of the players these games can be classified as follows: (a) turn-based (players make moves in turns); and (b) concurrent (players make moves simultaneously). On the basis of the information available to the players these games can be classified as follows: (a) perfect-information (players have perfect view of the game); and (b) partial-information (players have partial view of the game). In this talk we will consider all these classes of games with reachability objectives, where the goal of one player is to reach a set of target vertices of the graph, and the goal of the opponent player is to prevent the player from reaching the target. We will survey the results for various classes of games, and the results range from linear time decision algorithms to EXPTIME-complete problems to undecidable problems.},
author = {Chatterjee, Krishnendu},
editor = {Delzanno, Giorgo and Potapov, Igor},
location = {Genoa, Italy},
pages = {1 -- 1},
publisher = {Springer},
title = {{Graph games with reachability objectives}},
doi = {10.1007/978-3-642-24288-5_1},
volume = {6945},
year = {2011},
}
@inproceedings{3345,
abstract = {We consider Markov Decision Processes (MDPs) with mean-payoff parity and energy parity objectives. In system design, the parity objective is used to encode ω-regular specifications, and the mean-payoff and energy objectives can be used to model quantitative resource constraints. The energy condition re- quires that the resource level never drops below 0, and the mean-payoff condi- tion requires that the limit-average value of the resource consumption is within a threshold. While these two (energy and mean-payoff) classical conditions are equivalent for two-player games, we show that they differ for MDPs. We show that the problem of deciding whether a state is almost-sure winning (i.e., winning with probability 1) in energy parity MDPs is in NP ∩ coNP, while for mean- payoff parity MDPs, the problem is solvable in polynomial time, improving a recent PSPACE bound.},
author = {Chatterjee, Krishnendu and Doyen, Laurent},
location = {Warsaw, Poland},
pages = {206 -- 218},
publisher = {Springer},
title = {{Energy and mean-payoff parity Markov Decision Processes}},
doi = {10.1007/978-3-642-22993-0_21},
volume = {6907},
year = {2011},
}
@inproceedings{3346,
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 k reward 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 single-objective case, both randomization and memory are necessary for strategies, and that finite-memory randomized strategies are sufficient. Under the satisfaction objective, in contrast to the single-objective case, infinite memory is necessary for strategies, and that randomized memoryless strategies are sufficient for epsilon-approximation, for all epsilon>;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 epsilon-approximated in time polynomial in the size of the MDP and 1/epsilon, and exponential in the number of reward functions, for all epsilon>;0. Our results also reveal flaws in previous work for MDPs with multiple mean-payoff functions under the expectation objective, correct the flaws and obtain improved results.},
author = {Brázdil, Tomáš and Brožek, Václav and Chatterjee, Krishnendu and Forejt, Vojtěch and Kučera, Antonín},
location = {Toronto, Canada},
publisher = {IEEE},
title = {{Two views on multiple mean payoff objectives in Markov Decision Processes}},
doi = {10.1109/LICS.2011.10},
year = {2011},
}
@inproceedings{3347,
abstract = {The class of omega-regular languages provides a robust specification language in verification. Every omega-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens "eventually". Finitary liveness was proposed by Alur and Henzinger as a stronger formulation of liveness. It requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider automata with finitary acceptance conditions defined by finitary Buchi, parity and Streett languages. We study languages expressible by such automata: we give their topological complexity and present a regular-expression characterization. We compare the expressive power of finitary automata and give optimal algorithms for classical decisions questions. We show that the finitary languages are Sigma 2-complete; we present a complete picture of the expressive power of various classes of automata with finitary and infinitary acceptance conditions; we show that the languages defined by finitary parity automata exactly characterize the star-free fragment of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete and universality as well as language inclusion are PSPACE-complete for finitary parity and Streett automata.},
author = {Chatterjee, Krishnendu and Fijalkow, Nathanaël},
location = {Tarragona, Spain},
pages = {216 -- 226},
publisher = {Springer},
title = {{Finitary languages}},
doi = {10.1007/978-3-642-21254-3_16},
volume = {6638},
year = {2011},
}
@inproceedings{3348,
abstract = {We study synthesis of controllers for real-time systems, where the objective is to stay in a given safe set. The problem is solved by obtaining winning strategies in the setting of concurrent two-player timed automaton games with safety objectives. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a zeno run. We construct winning strategies for the controller which require access only to (1) the system clocks (thus, controllers which require their own internal infinitely precise clocks are not necessary), and (2) a linear (in the number of clocks) number of memory bits. Precisely, we show that for safety objectives, a memory of size (3 · |C|+lg(|C|+1)) bits suffices for winning controller strategies, where C is the set of clocks of the timed automaton game, significantly improving the previous known exponential bound. We also settle the open question of whether winning region controller strategies require memory for safety objectives by showing with an example the necessity of memory for region strategies to win for safety objectives.},
author = {Chatterjee, Krishnendu and Prabhu, Vinayak},
location = {Chicago, USA},
pages = {221 -- 230},
publisher = {Springer},
title = {{Synthesis of memory efficient real time controllers for safety objectives}},
doi = {10.1145/1967701.1967734},
year = {2011},
}
@inproceedings{3349,
abstract = {Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model various open systems in computer science, as for instance turn-based or concurrent moves, and deterministic or stochastic transitions. In this paper, we are interested in turn-based games, and specifically in deterministic parity games and stochastic reachability games (also known as simple stochastic games). We present a simple, direct and efficient reduction from deterministic parity games to simple stochastic games: it yields an arena whose size is linear up to a logarithmic factor in size of the original arena.},
author = {Chatterjee, Krishnendu and Fijalkow, Nathanaël},
location = {Minori, Italy},
pages = {74 -- 86},
publisher = {EPTCS},
title = {{A reduction from parity games to simple stochastic games}},
doi = {10.4204/EPTCS.54.6},
volume = {54},
year = {2011},
}
@inproceedings{3350,
abstract = {A controller for a discrete game with ω-regular objectives requires attention if, intuitively, it requires measuring the state and switching from the current control action. Minimum attention controllers are preferable in modern shared implementations of cyber-physical systems because they produce the least burden on system resources such as processor time or communication bandwidth. We give algorithms to compute minimum attention controllers for ω-regular objectives in imperfect information discrete two-player games. We show a polynomial-time reduction from minimum attention controller synthesis to synthesis of controllers for mean-payoff parity objectives in games of incomplete information. This gives an optimal EXPTIME-complete synthesis algorithm. We show that the minimum attention controller problem is decidable for infinite state systems with finite bisimulation quotients. In particular, the problem is decidable for timed and rectangular automata.},
author = {Chatterjee, Krishnendu and Majumdar, Ritankar},
editor = {Fahrenberg, Uli and Tripakis, Stavros},
location = {Aalborg, Denmark},
pages = {145 -- 159},
publisher = {Springer},
title = {{Minimum attention controller synthesis for omega regular objectives}},
doi = {10.1007/978-3-642-24310-3_11},
volume = {6919},
year = {2011},
}
@inproceedings{3351,
abstract = {In two-player games on graph, the players construct an infinite path through the game graph and get a reward computed by a payoff function over infinite paths. Over weighted graphs, the typical and most studied payoff functions compute the limit-average or the discounted sum of the rewards along the path. Besides their simple definition, these two payoff functions enjoy the property that memoryless optimal strategies always exist. In an attempt to construct other simple payoff functions, we define a class of payoff functions which compute an (infinite) weighted average of the rewards. This new class contains both the limit-average and the discounted sum functions, and we show that they are the only members of this class which induce memoryless optimal strategies, showing that there is essentially no other simple payoff functions.},
author = {Chatterjee, Krishnendu and Doyen, Laurent and Singh, Rohit},
editor = {Owe, Olaf and Steffen, Martin and Telle, Jan Arne},
location = {Oslo, Norway},
pages = {148 -- 159},
publisher = {Springer},
title = {{On memoryless quantitative objectives}},
doi = {10.1007/978-3-642-22953-4_13},
volume = {6914},
year = {2011},
}
@article{3354,
abstract = {We consider two-player games played on a finite state space for an infinite number of rounds. The games are concurrent: 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. We consider ω-regular winning conditions specified as parity objectives. Both players are allowed to use randomization when choosing their moves. We study the computation of the limit-winning set of states, consisting of the states where the sup-inf value of the game for player 1 is 1: in other words, a state is limit-winning if player 1 can ensure a probability of winning arbitrarily close to 1. We show that the limit-winning set can be computed in O(n2d+2) time, where n is the size of the game structure and 2d is the number of priorities (or colors). The membership problem of whether a state belongs to the limit-winning set can be decided in NP ∩ coNP. While this complexity is the same as for the simpler class of turn-based parity games, where in each state only one of the two players has a choice of moves, our algorithms are considerably more involved than those for turn-based games. This is because concurrent games do not satisfy two of the most fundamental properties of turn-based parity games. First, in concurrent games limit-winning strategies require randomization; and second, they require infinite memory.},
author = {Chatterjee, Krishnendu and De Alfaro, Luca and Henzinger, Thomas A},
journal = {ACM Transactions on Computational Logic (TOCL)},
number = {4},
publisher = {ACM},
title = {{Qualitative concurrent parity games}},
doi = {10.1145/1970398.1970404},
volume = {12},
year = {2011},
}
@inproceedings{3356,
abstract = {There is recently a significant effort to add quantitative objectives to formal verification and synthesis. We introduce and investigate the extension of temporal logics with quantitative atomic assertions, aiming for a general and flexible framework for quantitative-oriented specifications. In the heart of quantitative objectives lies the accumulation of values along a computation. It is either the accumulated summation, as with the energy objectives, or the accumulated average, as with the mean-payoff objectives. We investigate the extension of temporal logics with the prefix-accumulation assertions Sum(v) ≥ c and Avg(v) ≥ c, where v is a numeric variable of the system, c is a constant rational number, and Sum(v) and Avg(v) denote the accumulated sum and average of the values of v from the beginning of the computation up to the current point of time. We also allow the path-accumulation assertions LimInfAvg(v) ≥ c and LimSupAvg(v) ≥ c, referring to the average value along an entire computation. We study the border of decidability for extensions of various temporal logics. In particular, we show that extending the fragment of CTL that has only the EX, EF, AX, and AG temporal modalities by prefix-accumulation assertions and extending LTL with path-accumulation assertions, result in temporal logics whose model-checking problem is decidable. The extended logics allow to significantly extend the currently known energy and mean-payoff objectives. Moreover, the prefix-accumulation assertions may be refined with "controlled-accumulation", allowing, for example, to specify constraints on the average waiting time between a request and a grant. On the negative side, we show that the fragment we point to is, in a sense, the maximal logic whose extension with prefix-accumulation assertions permits a decidable model-checking procedure. Extending a temporal logic that has the EG or EU modalities, and in particular CTL and LTL, makes the problem undecidable.},
author = {Boker, Udi and Chatterjee, Krishnendu and Henzinger, Thomas A and Kupferman, Orna},
location = {Toronto, Canada},
publisher = {IEEE},
title = {{Temporal specifications with accumulative values}},
doi = {10.1109/LICS.2011.33},
year = {2011},
}
@inproceedings{3357,
abstract = {We consider two-player graph games whose objectives are request-response condition, i.e conjunctions of conditions of the form "if a state with property Rq is visited, then later a state with property Rp is visited". The winner of such games can be decided in EXPTIME and the problem is known to be NP-hard. In this paper, we close this gap by showing that this problem is, in fact, EXPTIME-complete. We show that the problem becomes PSPACE-complete if we only consider games played on DAGs, and NP-complete or PTIME-complete if there is only one player (depending on whether he wants to enforce or spoil the request-response condition). We also present near-optimal bounds on the memory needed to design winning strategies for each player, in each case.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Horn, Florian},
editor = {Dediu, Adrian-Horia and Inenaga, Shunsuke and Martín-Vide, Carlos},
location = {Tarragona, Spain},
pages = {227 -- 237},
publisher = {Springer},
title = {{The complexity of request-response games}},
doi = {10.1007/978-3-642-21254-3_17},
volume = {6638},
year = {2011},
}
@inproceedings{3361,
abstract = {In this paper, we investigate the computational complexity of quantitative information flow (QIF) problems. Information-theoretic quantitative relaxations of noninterference (based on Shannon entropy)have been introduced to enable more fine-grained reasoning about programs in situations where limited information flow is acceptable. The QIF bounding problem asks whether the information flow in a given program is bounded by a constant $d$. Our first result is that the QIF bounding problem is PSPACE-complete. The QIF memoryless synthesis problem asks whether it is possible to resolve nondeterministic choices in a given partial program in such a way that in the resulting deterministic program, the quantitative information flow is bounded by a given constant $d$. Our second result is that the QIF memoryless synthesis problem is also EXPTIME-complete. The QIF memoryless synthesis problem generalizes to QIF general synthesis problem which does not impose the memoryless requirement (that is, by allowing the synthesized program to have more variables then the original partial program). Our third result is that the QIF general synthesis problem is EXPTIME-hard.},
author = {Cerny, Pavol and Chatterjee, Krishnendu and Henzinger, Thomas A},
location = {Cernay-la-Ville, France},
pages = {205 -- 217},
publisher = {IEEE},
title = {{The complexity of quantitative information flow problems}},
doi = {10.1109/CSF.2011.21},
year = {2011},
}
@unpublished{3363,
abstract = {We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, Büchi, coBüchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs for probabilistic finite automata and present a complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Tracol, Mathieu},
pages = {19},
publisher = {ArXiv},
title = {{The decidability frontier for probabilistic automata on infinite words}},
year = {2011},
}