@article{717, abstract = {We consider finite-state and recursive game graphs with multidimensional mean-payoff objectives. In recursive games two types of strategies are relevant: global strategies and modular strategies. Our contributions are: (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 weights are fixed; whereas for arbitrary dimensions the problem is coNP-complete. (2) We show that one-player recursive games with multidimensional mean-payoff objectives can be solved in polynomial time. Both above algorithms are based on hyperplane separation technique. (3) For recursive games we show that under modular strategies the multidimensional problem is undecidable. We show that if the number of modules, exits, and the maximal absolute value of the weights are fixed, then one-dimensional recursive mean-payoff games under modular strategies can be solved in polynomial time, whereas for unbounded number of exits or modules the problem is NP-hard.}, author = {Chatterjee, Krishnendu and Velner, Yaron}, journal = {Journal of Computer and System Sciences}, pages = {236 -- 259}, publisher = {Academic Press}, title = {{Hyperplane separation technique for multidimensional mean-payoff games}}, doi = {10.1016/j.jcss.2017.04.005}, volume = {88}, year = {2017}, } @article{719, abstract = {The ubiquity of computation in modern machines and devices imposes a need to assert the correctness of their behavior. Especially in the case of safety-critical systems, their designers need to take measures that enforce their safe operation. Formal methods has emerged as a research field that addresses this challenge: by rigorously proving that all system executions adhere to their specifications, the correctness of an implementation under concern can be assured. To achieve this goal, a plethora of techniques are nowadays available, all of which are optimized for different system types and application domains.}, author = {Chatterjee, Krishnendu and Ehlers, Rüdiger}, issn = {0001-5903}, journal = {Acta Informatica}, number = {6}, pages = {543 -- 544}, publisher = {Springer}, title = {{Special issue: Synthesis and SYNT 2014}}, doi = {10.1007/s00236-017-0299-0}, volume = {54}, year = {2017}, } @article{744, abstract = {In evolutionary game theory interactions between individuals are often assumed obligatory. However, in many real-life situations, individuals can decide to opt out of an interaction depending on the information they have about the opponent. We consider a simple evolutionary game theoretic model to study such a scenario, where at each encounter between two individuals the type of the opponent (cooperator/defector) is known with some probability, and where each individual either accepts or opts out of the interaction. If the type of the opponent is unknown, a trustful individual accepts the interaction, whereas a suspicious individual opts out of the interaction. If either of the two individuals opt out both individuals remain without an interaction. We show that in the prisoners dilemma optional interactions along with suspicious behaviour facilitates the emergence of trustful cooperation.}, author = {Priklopil, Tadeas and Chatterjee, Krishnendu and Nowak, Martin}, issn = {0022-5193}, journal = { Journal of Theoretical Biology}, pages = {64 -- 72}, publisher = {Elsevier}, title = {{Optional interactions and suspicious behaviour facilitates trustful cooperation in prisoners dilemma}}, doi = {10.1016/j.jtbi.2017.08.025}, volume = {433}, year = {2017}, } @inproceedings{949, abstract = {The notion of treewidth of graphs has been exploited for faster algorithms for several problems arising in verification and program analysis. Moreover, various notions of balanced tree decompositions have been used for improved algorithms supporting dynamic updates and analysis of concurrent programs. In this work, we present a tool for constructing tree-decompositions of CFGs obtained from Java methods, which is implemented as an extension to the widely used Soot framework. The experimental results show that our implementation on real-world Java benchmarks is very efficient. Our tool also provides the first implementation for balancing tree-decompositions. In summary, we present the first tool support for exploiting treewidth in the static analysis problems on Java programs.}, author = {Chatterjee, Krishnendu and Goharshady, Amir and Pavlogiannis, Andreas}, editor = {D'Souza, Deepak}, issn = {0302-9743}, location = {Pune, India}, pages = {59 -- 66}, publisher = {Springer}, title = {{JTDec: A tool for tree decompositions in soot}}, doi = {10.1007/978-3-319-68167-2_4}, volume = {10482}, year = {2017}, } @inproceedings{639, abstract = {We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of non-recursive programs. First, we apply ranking functions to recursion, resulting in measure functions, and show that they provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in non-polynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas’ Lemma, and Handelman’s Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form O(n log n) as well as O(nr) where r is not an integer. We present experimental results to demonstrate that our approach can efficiently obtain worst-case bounds of classical recursive algorithms such as Merge-Sort, Closest-Pair, Karatsuba’s algorithm and Strassen’s algorithm.}, author = {Chatterjee, Krishnendu and Fu, Hongfei and Goharshady, Amir}, editor = {Majumdar, Rupak and Kunčak, Viktor}, isbn = {978-331963389-3}, location = {Heidelberg, Germany}, pages = {41 -- 63}, publisher = {Springer}, title = {{Non-polynomial worst case analysis of recursive programs}}, doi = {10.1007/978-3-319-63390-9_3}, volume = {10427}, year = {2017}, } @inproceedings{1090, abstract = { While weighted automata provide a natural framework to express quantitative properties, many basic properties like average response time cannot be expressed with weighted automata. Nested weighted automata extend weighted automata and consist of a master automaton and a set of slave automata that are invoked by the master automaton. Nested weighted automata are strictly more expressive than weighted automata (e.g., average response time can be expressed with nested weighted automata), but the basic decision questions have higher complexity (e.g., for deterministic automata, the emptiness question for nested weighted automata is PSPACE-hard, whereas the corresponding complexity for weighted automata is PTIME). We consider a natural subclass of nested weighted automata where at any point at most a bounded number k of slave automata can be active. We focus on automata whose master value function is the limit average. We show that these nested weighted automata with bounded width are strictly more expressive than weighted automata (e.g., average response time with no overlapping requests can be expressed with bound k=1, but not with non-nested weighted automata). We show that the complexity of the basic decision problems (i.e., emptiness and universality) for the subclass with k constant matches the complexity for weighted automata. Moreover, when k is part of the input given in unary we establish PSPACE-completeness.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, location = {Krakow; Poland}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Nested weighted limit-average automata of bounded width}}, doi = {10.4230/LIPIcs.MFCS.2016.24}, volume = {58}, year = {2016}, } @inproceedings{1093, abstract = {We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results. }, author = {Daca, Przemyslaw and Henzinger, Thomas A and Kretinsky, Jan and Petrov, Tatjana}, location = {Quebec City; Canada}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Linear distances between Markov chains}}, doi = {10.4230/LIPIcs.CONCUR.2016.20}, volume = {59}, year = {2016}, } @inproceedings{1138, abstract = {Automata with monitor counters, where the transitions do not depend on counter values, and nested weighted automata are two expressive automata-theoretic frameworks for quantitative properties. For a well-studied and wide class of quantitative functions, we establish that automata with monitor counters and nested weighted automata are equivalent. We study for the first time such quantitative automata under probabilistic semantics. We show that several problems that are undecidable for the classical questions of emptiness and universality become decidable under the probabilistic semantics. We present a complete picture of decidability for such automata, and even an almost-complete picture of computational complexity, for the probabilistic questions we consider. © 2016 ACM.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, booktitle = {Proceedings of the 31st Annual ACM/IEEE Symposium}, location = {New York, NY, USA}, pages = {76 -- 85}, publisher = {IEEE}, title = {{Quantitative automata under probabilistic semantics}}, doi = {10.1145/2933575.2933588}, year = {2016}, } @inproceedings{1140, abstract = {Given a model of a system and an objective, the model-checking question asks whether the model satisfies the objective. We study polynomial-time problems in two classical models, graphs and Markov Decision Processes (MDPs), with respect to several fundamental -regular objectives, e.g., Rabin and Streett objectives. For many of these problems the best-known upper bounds are quadratic or cubic, yet no super-linear lower bounds are known. In this work our contributions are two-fold: First, we present several improved algorithms, and second, we present the first conditional super-linear lower bounds based on widely believed assumptions about the complexity of CNF-SAT and combinatorial Boolean matrix multiplication. A separation result for two models with respect to an objective means a conditional lower bound for one model that is strictly higher than the existing upper bound for the other model, and similarly for two objectives with respect to a model. Our results establish the following separation results: (1) A separation of models (graphs and MDPs) for disjunctive queries of reachability and Büchi objectives. (2) Two kinds of separations of objectives, both for graphs and MDPs, namely, (2a) the separation of dual objectives such as Streett/Rabin objectives, and (2b) the separation of conjunction and disjunction of multiple objectives of the same type such as safety, Büchi, and coBüchi. In summary, our results establish the first model and objective separation results for graphs and MDPs for various classical -regular objectives. Quite strikingly, we establish conditional lower bounds for the disjunction of objectives that are strictly higher than the existing upper bounds for the conjunction of the same objectives. © 2016 ACM.}, author = {Chatterjee, Krishnendu and Dvoák, Wolfgang and Henzinger, Monika H and Loitzenbauer, Veronika}, booktitle = {Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science}, location = {New York, NY, USA}, pages = {197 -- 206}, publisher = {IEEE}, title = {{Model and objective separation with conditional lower bounds: disjunction is harder than conjunction}}, doi = {10.1145/2933575.2935304}, year = {2016}, } @inproceedings{1166, abstract = {POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIMEcomplete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach. © 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.}, author = {Chatterjee, Krishnendu and Chmelik, Martin and Davies, Jessica}, booktitle = {Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence}, location = {Phoenix, AZ, United States}, pages = {3225 -- 3232}, publisher = {AAAI Press}, title = {{A symbolic SAT based algorithm for almost sure reachability with small strategies in POMDPs}}, doi = {10.1609/aaai.v30i1.10422}, volume = {2016}, year = {2016}, } @inproceedings{1182, abstract = {Balanced knockout tournaments are ubiquitous in sports competitions and are also used in decisionmaking and elections. The traditional computational question, that asks to compute a draw (optimal draw) that maximizes the winning probability for a distinguished player, has received a lot of attention. Previous works consider the problem where the pairwise winning probabilities are known precisely, while we study how robust is the winning probability with respect to small errors in the pairwise winning probabilities. First, we present several illuminating examples to establish: (a) there exist deterministic tournaments (where the pairwise winning probabilities are 0 or 1) where one optimal draw is much more robust than the other; and (b) in general, there exist tournaments with slightly suboptimal draws that are more robust than all the optimal draws. The above examples motivate the study of the computational problem of robust draws that guarantee a specified winning probability. Second, we present a polynomial-time algorithm for approximating the robustness of a draw for sufficiently small errors in pairwise winning probabilities, and obtain that the stated computational problem is NP-complete. We also show that two natural cases of deterministic tournaments where the optimal draw could be computed in polynomial time also admit polynomial-time algorithms to compute robust optimal draws.}, author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Tkadlec, Josef}, location = {New York, NY, USA}, pages = {172 -- 179}, publisher = {AAAI Press}, title = {{Robust draws in balanced knockout tournaments}}, volume = {2016-January}, year = {2016}, } @article{1200, author = {Hilbe, Christian and Traulsen, Arne}, journal = {Physics of Life Reviews}, pages = {29 -- 31}, publisher = {Elsevier}, title = {{Only the combination of mathematics and agent based simulations can leverage the full potential of evolutionary modeling: Comment on “Evolutionary game theory using agent-based methods” by C. Adami, J. Schossau and A. Hintze}}, doi = {10.1016/j.plrev.2016.10.004}, volume = {19}, year = {2016}, } @inproceedings{1245, abstract = {To facilitate collaboration in massive online classrooms, instructors must make many decisions. For instance, the following parameters need to be decided when designing a peer-feedback system where students review each others' essays: the number of students each student must provide feedback to, an algorithm to map feedback providers to receivers, constraints that ensure students do not become free-riders (receiving feedback but not providing it), the best times to receive feedback to improve learning etc. While instructors can answer these questions by running experiments or invoking past experience, game-theoretic models with data from online learning platforms can identify better initial designs for further improvements. As an example, we explore the design space of a peer feedback system by modeling it using game theory. Our simulations show that incentivizing students to provide feedback requires the value obtained from receiving a feedback to exceed the cost of providing it by a large factor (greater than 7). Furthermore, hiding feedback from low-effort students incentivizes them to provide more feedback.}, author = {Pandey, Vineet and Chatterjee, Krishnendu}, booktitle = {Proceedings of the ACM Conference on Computer Supported Cooperative Work}, location = {San Francisco, CA, USA}, number = {Februar-2016}, pages = {365 -- 368}, publisher = {ACM}, title = {{Game-theoretic models identify useful principles for peer collaboration in online learning platforms}}, doi = {10.1145/2818052.2869122}, volume = {26}, year = {2016}, } @article{1322, abstract = {Direct reciprocity is a major mechanism for the evolution of cooperation. Several classical studies have suggested that humans should quickly learn to adopt reciprocal strategies to establish mutual cooperation in repeated interactions. On the other hand, the recently discovered theory of ZD strategies has found that subjects who use extortionate strategies are able to exploit and subdue cooperators. Although such extortioners have been predicted to succeed in any population of adaptive opponents, theoretical follow-up studies questioned whether extortion can evolve in reality. However, most of these studies presumed that individuals have similar strategic possibilities and comparable outside options, whereas asymmetries are ubiquitous in real world applications. Here we show with a model and an economic experiment that extortionate strategies readily emerge once subjects differ in their strategic power. Our experiment combines a repeated social dilemma with asymmetric partner choice. In our main treatment there is one randomly chosen group member who is unilaterally allowed to exchange one of the other group members after every ten rounds of the social dilemma. We find that this asymmetric replacement opportunity generally promotes cooperation, but often the resulting payoff distribution reflects the underlying power structure. Almost half of the subjects in a better strategic position turn into extortioners, who quickly proceed to exploit their peers. By adapting their cooperation probabilities consistent with ZD theory, extortioners force their co-players to cooperate without being similarly cooperative themselves. Comparison to non-extortionate players under the same conditions indicates a substantial net gain to extortion. Our results thus highlight how power asymmetries can endanger mutually beneficial interactions, and transform them into exploitative relationships. In particular, our results indicate that the extortionate strategies predicted from ZD theory could play a more prominent role in our daily interactions than previously thought.}, author = {Hilbe, Christian and Hagel, Kristin and Milinski, Manfred}, journal = {PLoS One}, number = {10}, publisher = {Public Library of Science}, title = {{Asymmetric power boosts extortion in an economic experiment}}, doi = {10.1371/journal.pone.0163867}, volume = {11}, year = {2016}, } @inproceedings{1324, abstract = {DEC-POMDPs extend POMDPs to a multi-agent setting, where several agents operate in an uncertain environment independently to achieve a joint objective. DEC-POMDPs have been studied with finite-horizon and infinite-horizon discounted-sum objectives, and there exist solvers both for exact and approximate solutions. In this work we consider Goal-DEC-POMDPs, where given a set of target states, the objective is to ensure that the target set is reached with minimal cost. We consider the indefinite-horizon (infinite-horizon with either discounted-sum, or undiscounted-sum, where absorbing goal states have zero-cost) problem. We present a new and novel method to solve the problem that extends methods for finite-horizon DEC-POMDPs and the RTDP-Bel approach for POMDPs. We present experimental results on several examples, and show that our approach presents promising results. Copyright }, author = {Chatterjee, Krishnendu and Chmelik, Martin}, booktitle = {Proceedings of the Twenty-Sixth International Conference on Automated Planning and Scheduling}, location = {London, United Kingdom}, pages = {88 -- 96}, publisher = {AAAI Press}, title = {{Indefinite-horizon reachability in Goal-DEC-POMDPs}}, doi = {10.1609/icaps.v26i1.13737}, volume = {2016}, year = {2016}, } @inproceedings{1325, abstract = {We study graphs and two-player games in which rewards are assigned to states, and the goal of the players is to satisfy or dissatisfy certain property of the generated outcome, given as a mean payoff property. Since the notion of mean-payoff does not reflect possible fluctuations from the mean-payoff along a run, we propose definitions and algorithms for capturing the stability of the system, and give algorithms for deciding if a given mean payoff and stability objective can be ensured in the system.}, author = {Brázdil, Tomáš and Forejt, Vojtěch and Kučera, Antonín and Novotny, Petr}, location = {Quebec City, Canada}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Stability in graphs and games}}, doi = {10.4230/LIPIcs.CONCUR.2016.10}, volume = {59}, year = {2016}, } @inproceedings{1326, abstract = {Energy Markov Decision Processes (EMDPs) are finite-state Markov decision processes where each transition is assigned an integer counter update and a rational payoff. An EMDP configuration is a pair s(n), where s is a control state and n is the current counter value. The configurations are changed by performing transitions in the standard way. We consider the problem of computing a safe strategy (i.e., a strategy that keeps the counter non-negative) which maximizes the expected mean payoff. }, author = {Brázdil, Tomáš and Kučera, Antonín and Novotny, Petr}, location = {Chiba, Japan}, pages = {32 -- 49}, publisher = {Springer}, title = {{Optimizing the expected mean payoff in Energy Markov Decision Processes}}, doi = {10.1007/978-3-319-46520-3_3}, volume = {9938}, year = {2016}, } @inproceedings{1327, abstract = {We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize the expected total cost until the target set is reached. We extend the traditional framework of POMDPs to model energy consumption, which represents a hard constraint. The energy levels may increase and decrease with transitions, and the hard constraint requires that the energy level must remain positive in all steps till the target is reached. First, we present a novel algorithm for solving POMDPs with energy levels, developing on existing POMDP solvers and using RTDP as its main method. Our second contribution is related to policy representation. For larger POMDP instances the policies computed by existing solvers are too large to be understandable. We present an automated procedure based on machine learning techniques that automatically extracts important decisions of the policy allowing us to compute succinct human readable policies. Finally, we show experimentally that our algorithm performs well and computes succinct policies on a number of POMDP instances from the literature that were naturally enhanced with energy levels. }, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Chmelik, Martin and Gupta, Anchit and Novotny, Petr}, booktitle = {Proceedings of the 15th International Conference on Autonomous Agents and Multiagent Systems}, location = {Singapore}, pages = {1465 -- 1466}, publisher = {ACM}, title = {{Stochastic shortest path with energy constraints in POMDPs}}, year = {2016}, } @article{1333, abstract = {Social dilemmas force players to balance between personal and collective gain. In many dilemmas, such as elected governments negotiating climate-change mitigation measures, the decisions are made not by individual players but by their representatives. However, the behaviour of representatives in social dilemmas has not been investigated experimentally. Here inspired by the negotiations for greenhouse-gas emissions reductions, we experimentally study a collective-risk social dilemma that involves representatives deciding on behalf of their fellow group members. Representatives can be re-elected or voted out after each consecutive collective-risk game. Selfish players are preferentially elected and are hence found most frequently in the "representatives" treatment. Across all treatments, we identify the selfish players as extortioners. As predicted by our mathematical model, their steadfast strategies enforce cooperation from fair players who finally compensate almost completely the deficit caused by the extortionate co-players. Everybody gains, but the extortionate representatives and their groups gain the most.}, author = {Milinski, Manfred and Hilbe, Christian and Semmann, Dirk and Sommerfeld, Ralf and Marotzke, Jochem}, journal = {Nature Communications}, publisher = {Nature Publishing Group}, title = {{Humans choose representatives who enforce cooperation in social dilemmas through extortion}}, doi = {10.1038/ncomms10915}, volume = {7}, year = {2016}, } @inproceedings{1335, abstract = {In this paper we review various automata-theoretic formalisms for expressing quantitative properties. We start with finite-state Boolean automata that express the traditional regular properties. We then consider weighted ω-automata that can measure the average density of events, which finite-state Boolean automata cannot. However, even weighted ω-automata cannot express basic performance properties like average response time. We finally consider two formalisms of weighted ω-automata with monitors, where the monitors are either (a) counters or (b) weighted automata themselves. We present a translation result to establish that these two formalisms are equivalent. Weighted ω-automata with monitors generalize weighted ω-automata, and can express average response time property. They present a natural, robust, and expressive framework for quantitative specifications, with important decidable properties.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, location = {Edinburgh, United Kingdom}, pages = {23 -- 38}, publisher = {Springer}, title = {{Quantitative monitor automata}}, doi = {10.1007/978-3-662-53413-7_2}, volume = {9837}, year = {2016}, }