@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}, } @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}, } @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}, } @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}, } @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{5404, abstract = {We study finite-state two-player (zero-sum) concurrent mean-payoff games played on a 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 lie in FNP; (3) the approximation problem is at least as hard as the decision problem for simple stochastic games (for which NP and coNP is the long-standing best known bound). We show that the exact value can be expressed in the existential theory of the reals, and also establish square-root sum hardness for a related class of games.}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus}, issn = {2664-1690}, pages = {29}, publisher = {IST Austria}, title = {{The complexity of ergodic games}}, doi = {10.15479/AT:IST-2013-127-v1-1}, year = {2013}, } @misc{5405, 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) with only parity objectives, or with only mean-payoff objectives. We present an algorithm running in time O(d · n^{2d}·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}, issn = {2664-1690}, pages = {22}, publisher = {IST Austria}, title = {{Perfect-information stochastic mean-payoff parity games}}, doi = {10.15479/AT:IST-2013-128-v1-1}, year = {2013}, } @misc{5409, 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 timestamps. 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 delta away from the parameter, for delta>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 we show analogous decidability results for rectangular automata.}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Majumdar, Rupak}, issn = {2664-1690}, pages = {12}, publisher = {IST Austria}, title = {{Edit distance for timed automata}}, doi = {10.15479/AT:IST-2013-144-v1-1}, year = {2013}, } @inproceedings{1376, abstract = {We consider the distributed synthesis problem for temporal logic specifications. Traditionally, the problem has been studied for LTL, and the previous results show that the problem is decidable iff there is no information fork in the architecture. We consider the problem for fragments of LTL and our main results are as follows: (1) We show that the problem is undecidable for architectures with information forks even for the fragment of LTL with temporal operators restricted to next and eventually. (2) For specifications restricted to globally along with non-nested next operators, we establish decidability (in EXPSPACE) for star architectures where the processes receive disjoint inputs, whereas we establish undecidability for architectures containing an information fork-meet structure. (3) Finally, we consider LTL without the next operator, and establish decidability (NEXPTIME-complete) for all architectures for a fragment that consists of a set of safety assumptions, and a set of guarantees where each guarantee is a safety, reachability, or liveness condition.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan and Pavlogiannis, Andreas}, booktitle = {13th International Conference on Formal Methods in Computer-Aided Design}, location = {Portland, OR, United States}, pages = {18 -- 25}, publisher = {IEEE}, title = {{Distributed synthesis for LTL fragments}}, doi = {10.1109/FMCAD.2013.6679386}, year = {2013}, } @misc{5406, abstract = {We consider the distributed synthesis problem fortemporal logic specifications. Traditionally, the problem has been studied for LTL, and the previous results show that the problem is decidable iff there is no information fork in the architecture. We consider the problem for fragments of LTLand our main results are as follows: (1) We show that the problem is undecidable for architectures with information forks even for the fragment of LTL with temporal operators restricted to next and eventually. (2) For specifications restricted to globally along with non-nested next operators, we establish decidability (in EXPSPACE) for star architectures where the processes receive disjoint inputs, whereas we establish undecidability for architectures containing an information fork-meet structure. (3)Finally, we consider LTL without the next operator, and establish decidability (NEXPTIME-complete) for all architectures for a fragment that consists of a set of safety assumptions, and a set of guarantees where each guarantee is a safety, reachability, or liveness condition.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan and Pavlogiannis, Andreas}, issn = {2664-1690}, pages = {11}, publisher = {IST Austria}, title = {{Distributed synthesis for LTL Fragments}}, doi = {10.15479/AT:IST-2013-130-v1-1}, year = {2013}, } @misc{5408, abstract = {We consider two-player partial-observation stochastic games where player 1 has partial observation and player 2 has perfect observation. The winning condition we study are omega-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). While the qualitative analysis problems are known to be undecidable even for very special cases of parity objectives, they were shown to be decidable in 2EXPTIME under finite-memory strategies. 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}, issn = {2664-1690}, pages = {17}, publisher = {IST Austria}, title = {{The complexity of partial-observation stochastic parity games with finite-memory strategies}}, doi = {10.15479/AT:IST-2013-141-v1-1}, year = {2013}, } @misc{5410, abstract = {Board games, like Tic-Tac-Toe and CONNECT-4, play an important role not only in development of mathematical and logical skills, but also in emotional and social development. In this paper, we address the problem of generating targeted starting positions for such games. This can facilitate new approaches for bringing novice players to mastery, and also leads to discovery of interesting game variants. Our approach generates starting states of varying hardness levels for player 1 in a two-player board game, given rules of the board game, the desired number of steps required for player 1 to win, and the expertise levels of the two players. Our approach leverages symbolic methods and iterative simulation to efficiently search the extremely large state space. We present experimental results that include discovery of states of varying hardness levels for several simple grid-based board games. Also, the presence of such states for standard game variants like Tic-Tac-Toe on board size 4x4 opens up new games to be played that have not been played for ages since the default start state is heavily biased. }, author = {Ahmed, Umair and Chatterjee, Krishnendu and Gulwani, Sumit}, issn = {2664-1690}, pages = {13}, publisher = {IST Austria}, title = {{Automatic generation of alternative starting positions for traditional board games}}, doi = {10.15479/AT:IST-2013-146-v1-1}, 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}, } @misc{9749, 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}, publisher = {Public Library of Science}, title = {{Forgiver triumphs in alternating prisoner's dilemma }}, doi = {10.1371/journal.pone.0080814.s001}, year = {2013}, } @inproceedings{10902, abstract = {We consider how to edit strings from a source language so that the edited strings belong to a target language, where the languages are given as deterministic finite automata. Non-streaming (or offline) transducers perform edits given the whole source string. We show that the class of deterministic one-pass transducers with registers along with increment and min operation suffices for computing optimal edit distance, whereas the same class of transducers without the min operation is not sufficient. Streaming (or online) transducers perform edits as the letters of the source string are received. We present a polynomial time algorithm for the partial-repair problem that given a bound α asks for the construction of a deterministic streaming transducer (if one exists) that ensures that the ‘maximum fraction’ η of the strings of the source language are edited, within cost α, to the target language.}, author = {Chatterjee, Krishnendu and Chaubal, Siddhesh and Rubin, Sasha}, booktitle = {7th International Conference on Language and Automata Theory and Applications}, isbn = {9783642370632}, issn = {1611-3349}, location = {Bilbao, Spain}, pages = {214--225}, publisher = {Springer Nature}, title = {{How to travel between languages}}, doi = {10.1007/978-3-642-37064-9_20}, volume = {7810}, 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}, } @article{2858, abstract = {Tumor growth is caused by the acquisition of driver mutations, which enhance the net reproductive rate of cells. Driver mutations may increase cell division, reduce cell death, or allow cells to overcome density-limiting effects. We study the dynamics of tumor growth as one additional driver mutation is acquired. Our models are based on two-type branching processes that terminate in either tumor disappearance or tumor detection. In our first model, both cell types grow exponentially, with a faster rate for cells carrying the additional driver. We find that the additional driver mutation does not affect the survival probability of the lesion, but can substantially reduce the time to reach the detectable size if the lesion is slow growing. In our second model, cells lacking the additional driver cannot exceed a fixed carrying capacity, due to density limitations. In this case, the time to detection depends strongly on this carrying capacity. Our model provides a quantitative framework for studying tumor dynamics during different stages of progression. We observe that early, small lesions need additional drivers, while late stage metastases are only marginally affected by them. These results help to explain why additional driver mutations are typically not detected in fast-growing metastases.}, author = {Reiter, Johannes and Božić, Ivana and Allen, Benjamin and Chatterjee, Krishnendu and Nowak, Martin}, journal = {Evolutionary Applications}, number = {1}, pages = {34 -- 45}, publisher = {Wiley-Blackwell}, title = {{The effect of one additional driver mutation on tumor progression}}, doi = {10.1111/eva.12020}, volume = {6}, year = {2013}, } @article{2816, abstract = {In solid tumors, targeted treatments can lead to dramatic regressions, but responses are often short-lived because resistant cancer cells arise. The major strategy proposed for overcoming resistance is combination therapy. We present a mathematical model describing the evolutionary dynamics of lesions in response to treatment. We first studied 20 melanoma patients receiving vemurafenib. We then applied our model to an independent set of pancreatic, colorectal, and melanoma cancer patients with metastatic disease. We find that dual therapy results in long-term disease control for most patients, if there are no single mutations that cause cross-resistance to both drugs; in patients with large disease burden, triple therapy is needed. We also find that simultaneous therapy with two drugs is much more effective than sequential therapy. Our results provide realistic expectations for the efficacy of new drug combinations and inform the design of trials for new cancer therapeutics.}, author = {Božić, Ivana and Reiter, Johannes and Allen, Benjamin and Antal, Tibor and Chatterjee, Krishnendu and Shah, Preya and Moon, Yo and Yaqubie, Amin and Kelly, Nicole and Le, Dung and Lipson, Evan and Chapman, Paul and Diaz, Luis and Vogelstein, Bert and Nowak, Martin}, journal = {eLife}, publisher = {eLife Sciences Publications}, title = {{Evolutionary dynamics of cancer in response to targeted combination therapy}}, doi = {10.7554/eLife.00747}, volume = {2}, year = {2013}, } @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{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{2820, abstract = {In this paper, we introduce the powerful framework of graph games for the analysis of real-time scheduling with firm deadlines. We introduce a novel instance of a partial-observation game that is suitable for this purpose, and prove decidability of all the involved decision problems. We derive a graph game that allows the automated computation of the competitive ratio (along with an optimal witness algorithm for the competitive ratio) and establish an NP-completeness proof for the graph game problem. For a given on-line algorithm, we present polynomial time solution for computing (i) the worst-case utility; (ii) the worst-case utility ratio w.r.t. a clairvoyant off-line algorithm; and (iii) the competitive ratio. A major strength of the proposed approach lies in its flexibility w.r.t. incorporating additional constraints on the adversary and/or the algorithm, including limited maximum or average load, finiteness of periods of overload, etc., which are easily added by means of additional instances of standard objective functions for graph games. }, author = {Chatterjee, Krishnendu and Kößler, Alexander and Schmid, Ulrich}, booktitle = {Proceedings of the 16th International conference on Hybrid systems: Computation and control}, isbn = {978-1-4503-1567-8 }, location = {Philadelphia, PA, United States}, pages = {163 -- 172}, publisher = {ACM}, title = {{Automated analysis of real-time scheduling using graph games}}, doi = {10.1145/2461328.2461356}, year = {2013}, } @inproceedings{2715, abstract = {We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning vertices from where the objective can be ensured with probability 1. We study for the first time the average case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average case running time is linear (as compared to the worst case linear number of iterations and quadratic time complexity). Second, for the average case analysis over all MDPs we show that the expected number of iterations is constant and the average case running time is linear (again as compared to the worst case linear number of iterations and quadratic time complexity). Finally we also show that given that all MDPs are equally likely, the probability that the classical algorithm requires more than constant number of iterations is exponentially small.}, author = {Chatterjee, Krishnendu and Joglekar, Manas and Shah, Nisarg}, location = {Hyderabad, India}, pages = {461 -- 473}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives}}, doi = {10.4230/LIPIcs.FSTTCS.2012.461}, volume = {18}, year = {2012}, } @inproceedings{10904, 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-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 VASS (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-François}, booktitle = {CONCUR 2012 - Concurrency Theory}, editor = {Koutny, Maciej and Ulidowski, Irek}, isbn = {9783642329395}, issn = {0302-9743}, location = {Newcastle upon Tyne, United Kingdom}, pages = {115--131}, publisher = {Springer}, title = {{Strategy synthesis for multi-dimensional quantitative objectives}}, doi = {10.1007/978-3-642-32940-1_10}, volume = {7454}, year = {2012}, } @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{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}, } @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}, } @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{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}, } @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}, } @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}, } @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}, } @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 H}, 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{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}, } @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}, } @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{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}, } @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}, } @inproceedings{10905, 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. While the existence of polynomial-time algorithms has been a major open problem for decades, 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 counter examples that show that many 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 graph structures need not help.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Krinninger, Sebastian and Nanongkai, Danupon}, booktitle = {Algorithms – ESA 2012}, isbn = {9783642330896}, issn = {1611-3349}, location = {Ljubljana, Slovenia}, pages = {301--312}, publisher = {Springer}, title = {{Polynomial-time algorithms for energy games with special weight structures}}, doi = {10.1007/978-3-642-33090-2_27}, volume = {7501}, 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}, } @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}, } @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}, } @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}, }