@inproceedings{1374, abstract = {We study two-player zero-sum games over infinite-state graphs equipped with ωB and finitary conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state graphs, memoryless strategies are sufficient for finitary Büchi, and finite-memory suffices for finitary parity games. We then study pushdown games with boundedness conditions, with two contributions. First we prove a collapse result for pushdown games with ωB-conditions, implying the decidability of solving these games. Second we consider pushdown games with finitary parity along with stack boundedness conditions, and show that solving these games is EXPTIME-complete.}, author = {Chatterjee, Krishnendu and Fijalkow, Nathanaël}, booktitle = {22nd EACSL Annual Conference on Computer Science Logic}, location = {Torino, Italy}, pages = {181 -- 196}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Infinite-state games with finitary conditions}}, doi = {10.4230/LIPIcs.CSL.2013.181}, volume = {23}, year = {2013}, } @inproceedings{2238, abstract = {We study the problem of achieving a given value in Markov decision processes (MDPs) with several independent discounted reward objectives. We consider a generalised version of discounted reward objectives, in which the amount of discounting depends on the states visited and on the objective. This definition extends the usual definition of discounted reward, and allows to capture the systems in which the value of different commodities diminish at different and variable rates. We establish results for two prominent subclasses of the problem, namely state-discount models where the discount factors are only dependent on the state of the MDP (and independent of the objective), and reward-discount models where they are only dependent on the objective (but not on the state of the MDP). For the state-discount models we use a straightforward reduction to expected total reward and show that the problem whether a value is achievable can be solved in polynomial time. For the reward-discount model we show that memory and randomisation of the strategies are required, but nevertheless that the problem is decidable and it is sufficient to consider strategies which after a certain number of steps behave in a memoryless way. For the general case, we show that when restricted to graphs (i.e. MDPs with no randomisation), pure strategies and discount factors of the form 1/n where n is an integer, the problem is in PSPACE and finite memory suffices for achieving a given value. We also show that when the discount factors are not of the form 1/n, the memory required by a strategy can be infinite. }, author = {Chatterjee, Krishnendu and Forejt, Vojtěch and Wojtczak, Dominik}, location = {Stellenbosch, South Africa}, pages = {228 -- 242}, publisher = {Springer}, title = {{Multi-objective discounted reward verification in graphs and MDPs}}, doi = {10.1007/978-3-642-45221-5_17}, volume = {8312}, year = {2013}, } @proceedings{2292, abstract = {This book constitutes the thoroughly refereed conference proceedings of the 38th International Symposium on Mathematical Foundations of Computer Science, MFCS 2013, held in Klosterneuburg, Austria, in August 2013. The 67 revised full papers presented together with six invited talks were carefully selected from 191 submissions. Topics covered include algorithmic game theory, algorithmic learning theory, algorithms and data structures, automata, formal languages, bioinformatics, complexity, computational geometry, computer-assisted reasoning, concurrency theory, databases and knowledge-based systems, foundations of computing, logic in computer science, models of computation, semantics and verification of programs, and theoretical issues in artificial intelligence.}, editor = {Chatterjee, Krishnendu and Sgall, Jiri}, isbn = {978-3-642-40312-5}, location = {Klosterneuburg, Austria}, pages = {VI -- 854}, publisher = {Springer}, title = {{Mathematical Foundations of Computer Science 2013}}, doi = {10.1007/978-3-642-40313-2}, volume = {8087}, year = {2013}, } @article{2299, abstract = {The standard hardware design flow involves: (a) design of an integrated circuit using a hardware description language, (b) extensive functional and formal verification, and (c) logical synthesis. However, the above-mentioned processes consume significant effort and time. An alternative approach is to use a formal specification language as a high-level hardware description language and synthesize hardware from formal specifications. Our work is a case study of the synthesis of the widely and industrially used AMBA AHB protocol from formal specifications. Bloem et al. presented the first formal specifications for the AMBA AHB Arbiter and synthesized the AHB Arbiter circuit. However, in the first formal specification some important assumptions were missing. Our contributions are as follows: (a) We present detailed formal specifications for the AHB Arbiter incorporating the missing details, and obtain significant improvements in the synthesis results (both with respect to the number of gates in the synthesized circuit and with respect to the time taken to synthesize the circuit), and (b) we present formal specifications to generate compact circuits for the remaining two main components of AMBA AHB, namely, AHB Master and AHB Slave. Thus with systematic description we are able to automatically and completely synthesize an important and widely used industrial protocol.}, author = {Godhal, Yashdeep and Chatterjee, Krishnendu and Henzinger, Thomas A}, journal = {International Journal on Software Tools for Technology Transfer}, number = {5-6}, pages = {585 -- 601}, publisher = {Springer}, title = {{Synthesis of AMBA AHB from formal specification: A case study}}, doi = {10.1007/s10009-011-0207-9}, volume = {15}, year = {2013}, } @inproceedings{2446, abstract = {The model-checking problem for probabilistic systems crucially relies on the translation of LTL to deterministic Rabin automata (DRW). Our recent Safraless translation [KE12, GKE12] for the LTL(F,G) fragment produces smaller automata as compared to the traditional approach. In this work, instead of DRW we consider deterministic automata with acceptance condition given as disjunction of generalized Rabin pairs (DGRW). The Safraless translation of LTL(F,G) formulas to DGRW results in smaller automata as compared to DRW. We present algorithms for probabilistic model-checking as well as game solving for DGRW conditions. Our new algorithms lead to improvement both in terms of theoretical bounds as well as practical evaluation. We compare PRISM with and without our new translation, and show that the new translation leads to significant improvements.}, author = {Chatterjee, Krishnendu and Gaiser, Andreas and Kretinsky, Jan}, location = {St. Petersburg, Russia}, pages = {559 -- 575}, publisher = {Springer}, title = {{Automata with generalized Rabin pairs for probabilistic model checking and LTL synthesis}}, doi = {10.1007/978-3-642-39799-8_37}, volume = {8044}, year = {2013}, } @inproceedings{2444, abstract = {We consider two core algorithmic problems for probabilistic verification: the maximal end-component decomposition and the almost-sure reachability set computation for Markov decision processes (MDPs). For MDPs with treewidth k, we present two improved static algorithms for both the problems that run in time O(n·k 2.38·2k ) and O(m·logn· k), respectively, where n is the number of states and m is the number of edges, significantly improving the previous known O(n·k·√n· k) bound for low treewidth. We also present decremental algorithms for both problems for MDPs with constant treewidth that run in amortized logarithmic time, which is a huge improvement over the previously known algorithms that require amortized linear time.}, author = {Chatterjee, Krishnendu and Ła̧Cki, Jakub}, location = {St. Petersburg, Russia}, pages = {543 -- 558}, publisher = {Springer}, title = {{Faster algorithms for Markov decision processes with low treewidth}}, doi = {10.1007/978-3-642-39799-8_36}, volume = {8044}, year = {2013}, } @article{2814, abstract = {We study the problem of generating a test sequence that achieves maximal coverage for a reactive system under test. We formulate the problem as a repeated game between the tester and the system, where the system state space is partitioned according to some coverage criterion and the objective of the tester is to maximize the set of partitions (or coverage goals) visited during the game. We show the complexity of the maximal coverage problem for non-deterministic systems is PSPACE-complete, but is NP-complete for deterministic systems. For the special case of non-deterministic systems with a re-initializing "reset" action, which represent running a new test input on a re-initialized system, we show that the complexity is coNP-complete. Our proof technique for reset games uses randomized testing strategies that circumvent the exponentially large memory requirement of deterministic testing strategies. We also discuss the memory requirement for deterministic strategies and extensions of our results to other models, such as pushdown systems and timed systems.}, author = {Chatterjee, Krishnendu and Alfaro, Luca and Majumdar, Ritankar}, journal = {International Journal of Foundations of Computer Science}, number = {2}, pages = {165 -- 185}, publisher = {World Scientific Publishing}, title = {{The complexity of coverage}}, doi = {10.1142/S0129054113400066}, volume = {24}, year = {2013}, } @article{2817, abstract = {The basic idea of evolutionary game theory is that payoff determines reproductive rate. Successful individuals have a higher payoff and produce more offspring. But in evolutionary and ecological situations there is not only reproductive rate but also carrying capacity. Individuals may differ in their exposure to density limiting effects. Here we explore an alternative approach to evolutionary game theory by assuming that the payoff from the game determines the carrying capacity of individual phenotypes. Successful strategies are less affected by density limitation (crowding) and reach higher equilibrium abundance. We demonstrate similarities and differences between our framework and the standard replicator equation. Our equation is defined on the positive orthant, instead of the simplex, but has the same equilibrium points as the replicator equation. Linear stability analysis produces the classical conditions for asymptotic stability of pure strategies, but the stability properties of internal equilibria can differ in the two frameworks. For example, in a two-strategy game with an internal equilibrium that is always stable under the replicator equation, the corresponding equilibrium can be unstable in the new framework resulting in a limit cycle.}, author = {Novak, Sebastian and Chatterjee, Krishnendu and Nowak, Martin}, journal = {Journal of Theoretical Biology}, pages = {26 -- 34}, publisher = {Elsevier}, title = {{Density games}}, doi = {10.1016/j.jtbi.2013.05.029}, volume = {334}, year = {2013}, } @inproceedings{2819, abstract = {We introduce quantatitive timed refinement metrics and quantitative timed simulation functions, incorporating zenoness checks, for timed systems. These functions assign positive real numbers between zero and infinity which quantify the timing mismatches between two timed systems, amongst non-zeno runs. We quantify timing mismatches in three ways: (1) the maximum timing mismatch that can arise, (2) the "steady-state" maximum timing mismatches, where initial transient timing mismatches are ignored; and (3) the (long-run) average timing mismatches amongst two systems. These three kinds of mismatches constitute three important types of timing differences. Our event times are the global times, measured from the start of the system execution, not just the time durations of individual steps. We present algorithms over timed automata for computing the three quantitative simulation functions to within any desired degree of accuracy. In order to compute the values of the quantitative simulation functions, we use a game theoretic formulation. We introduce two new kinds of objectives for two player games on finite state game graphs: (1) eventual debit-sum level objectives, and (2) average debit-sum level objectives. We present algorithms for computing the optimal values for these objectives for player 1, and then use these algorithms to compute the values of the quantitative timed simulation functions. }, author = {Chatterjee, Krishnendu and Prabhu, Vinayak}, booktitle = {Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control}, location = {Philadelphia, PA USA}, pages = {273 -- 282}, publisher = {Springer}, title = {{Quantitative timed simulation functions and refinement metrics for real-time systems}}, doi = {10.1145/2461328.2461370}, volume = {1}, year = {2013}, } @article{2824, abstract = {We study synthesis of controllers for real-time systems, where the objective is to stay in a given safe set. The problem is solved by obtaining winning strategies in the setting of concurrent two player timed automaton games with safety objectives. To prevent a player from winning by blocking time, we restrict each player to strategies that ensure that the player cannot be responsible for causing a Zeno run. We construct winning strategies for the controller which require access only to (1) the system clocks (thus, controllers which require their own internal infinitely precise clocks are not necessary), and (2) a logarithmic (in the number of clocks) number of memory bits (i.e. a linear number of memory states). Precisely, we show that for safety objectives, a memory of size (3 + lg (| C | + 1)) bits suffices for winning controller strategies, where C is the set of clocks of the timed automaton game, significantly improving the previous known exponential memory states bound. We also settle the open question of whether winning region-based strategies require memory for safety objectives by showing with an example the necessity of memory for such strategies to win for safety objectives. Finally, we show that the decision problem of determining if there exists a receptive player-1 winning strategy for safety objectives is EXPTIME-complete over timed automaton games.}, author = {Chatterjee, Krishnendu and Prabhu, Vinayak}, journal = {Information and Computation}, pages = {83--119}, publisher = {Elsevier}, title = {{Synthesis of memory-efficient, clock-memory free, and non-Zeno safety controllers for timed systems}}, doi = {10.1016/j.ic.2013.04.003}, volume = {228-229}, year = {2013}, } @article{2836, 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 and the trusted third party as path formulas in linear temporal logic and prove that the satisfaction of these objectives imply fairness; a property required of fair exchange protocols. We then show that weak (co-operative) co-synthesis and classical (strictly competitive) co-synthesis fail, whereas assume-guarantee synthesis (AGS) succeeds. We demonstrate the success of AGS as follows: (a) any solution of AGS is attack-free; no subset of participants can violate the objectives of the other participants; (b) the Asokan-Shoup-Waidner certified mail protocol that has known vulnerabilities is not a solution of AGS; (c) the Kremer-Markowitch non-repudiation protocol is a solution of AGS; and (d) AGS presents a new and symmetric fair non-repudiation protocol that is attack-free. To our knowledge this is the first application of synthesis to fair non-repudiation protocols, and our results show how synthesis can both automatically discover vulnerabilities in protocols and generate correct protocols. The solution to AGS can be computed efficiently as the secure equilibrium solution of three-player graph games. }, author = {Chatterjee, Krishnendu and Raman, Vishwanath}, journal = {Formal Aspects of Computing}, number = {4}, pages = {825 -- 859}, publisher = {Springer}, title = {{Assume-guarantee synthesis for digital contract signing}}, doi = {10.1007/s00165-013-0283-6}, volume = {26}, year = {2013}, } @article{2854, abstract = {We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. First, we present a simple proof of the fact that in concurrent reachability games, for all ε>0, memoryless ε-optimal strategies exist. A memoryless strategy is independent of the history of plays, and an ε-optimal strategy achieves the objective with probability within ε of the value of the game. In contrast to previous proofs of this fact, our proof is more elementary and more combinatorial. Second, we present a strategy-improvement (a.k.a. policy-iteration) algorithm for concurrent games with reachability objectives. Finally, we present a strategy-improvement algorithm for turn-based stochastic games (where each player selects moves in turns) with safety objectives. Our algorithms yield sequences of player-1 strategies which ensure probabilities of winning that converge monotonically (from below) to the value of the game. © 2012 Elsevier Inc.}, author = {Chatterjee, Krishnendu and De Alfaro, Luca and Henzinger, Thomas A}, journal = {Journal of Computer and System Sciences}, number = {5}, pages = {640 -- 657}, publisher = {Elsevier}, title = {{Strategy improvement for concurrent reachability and turn based stochastic safety games}}, doi = {10.1016/j.jcss.2012.12.001}, volume = {79}, year = {2013}, } @inproceedings{2886, abstract = {We focus on the realizability problem of Message Sequence Graphs (MSG), i.e. the problem whether a given MSG specification is correctly distributable among parallel components communicating via messages. This fundamental problem of MSG is known to be undecidable. We introduce a well motivated restricted class of MSG, so called controllable-choice MSG, and show that all its models are realizable and moreover it is decidable whether a given MSG model is a member of this class. In more detail, this class of MSG specifications admits a deadlock-free realization by overloading existing messages with additional bounded control data. We also show that the presented class is the largest known subclass of MSG that allows for deadlock-free realization.}, author = {Chmelik, Martin and Řehák, Vojtěch}, location = {Znojmo, Czech Republic}, pages = {118 -- 130}, publisher = {Springer}, title = {{Controllable-choice message sequence graphs}}, doi = {10.1007/978-3-642-36046-6_12}, volume = {7721}, year = {2013}, } @article{3116, abstract = {Multithreaded programs coordinate their interaction through synchronization primitives like mutexes and semaphores, which are managed by an OS-provided resource manager. We propose algorithms for the automatic construction of code-aware resource managers for multithreaded embedded applications. Such managers use knowledge about the structure and resource usage (mutex and semaphore usage) of the threads to guarantee deadlock freedom and progress while managing resources in an efficient way. Our algorithms compute managers as winning strategies in certain infinite games, and produce a compact code description of these strategies. We have implemented the algorithms in the tool Cynthesis. Given a multithreaded program in C, the tool produces C code implementing a code-aware resource manager. We show in experiments that Cynthesis produces compact resource managers within a few minutes on a set of embedded benchmarks with up to 6 threads. © 2012 Springer Science+Business Media, LLC.}, author = {Chatterjee, Krishnendu and De Alfaro, Luca and Faella, Marco and Majumdar, Ritankar and Raman, Vishwanath}, journal = {Formal Methods in System Design}, number = {2}, pages = {142 -- 174}, publisher = {Springer}, title = {{Code aware resource management}}, doi = {10.1007/s10703-012-0170-4}, volume = {42}, year = {2013}, } @article{2831, abstract = {We consider Markov decision processes (MDPs) with Büchi (liveness) objectives. We consider the problem of computing the set of almost-sure winning states from where the objective can be ensured with probability 1. Our contributions are as follows: First, we present the first subquadratic symbolic algorithm to compute the almost-sure winning set for MDPs with Büchi objectives; our algorithm takes O(n · √ m) symbolic steps as compared to the previous known algorithm that takes O(n 2) symbolic steps, where n is the number of states and m is the number of edges of the MDP. In practice MDPs have constant out-degree, and then our symbolic algorithm takes O(n · √ n) symbolic steps, as compared to the previous known O(n 2) symbolic steps algorithm. Second, we present a new algorithm, namely win-lose algorithm, with the following two properties: (a) the algorithm iteratively computes subsets of the almost-sure winning set and its complement, as compared to all previous algorithms that discover the almost-sure winning set upon termination; and (b) requires O(n · √ K) symbolic steps, where K is the maximal number of edges of strongly connected components (scc's) of the MDP. The win-lose algorithm requires symbolic computation of scc's. Third, we improve the algorithm for symbolic scc computation; the previous known algorithm takes linear symbolic steps, and our new algorithm improves the constants associated with the linear number of steps. In the worst case the previous known algorithm takes 5×n symbolic steps, whereas our new algorithm takes 4×n symbolic steps.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Joglekar, Manas and Shah, Nisarg}, journal = {Formal Methods in System Design}, number = {3}, pages = {301 -- 327}, publisher = {Springer}, title = {{Symbolic algorithms for qualitative analysis of Markov decision processes with Büchi objectives}}, doi = {10.1007/s10703-012-0180-2}, volume = {42}, year = {2013}, } @inproceedings{2279, abstract = {We consider two-player games played on weighted directed graphs with mean-payoff and total-payoff objectives, two classical quantitative objectives. While for single-dimensional games the complexity and memory bounds for both objectives coincide, we show that in contrast to multi-dimensional mean-payoff games that are known to be coNP-complete, multi-dimensional total-payoff games are undecidable. We introduce conservative approximations of these objectives, where the payoff is considered over a local finite window sliding along a play, instead of the whole play. For single dimension, we show that (i) if the window size is polynomial, deciding the winner takes polynomial time, and (ii) the existence of a bounded window can be decided in NP ∩ coNP, and is at least as hard as solving mean-payoff games. For multiple dimensions, we show that (i) the problem with fixed window size is EXPTIME-complete, and (ii) there is no primitive-recursive algorithm to decide the existence of a bounded window.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Randour, Mickael and Raskin, Jean}, location = {Hanoi, Vietnam}, pages = {118 -- 132}, publisher = {Springer}, title = {{Looking at mean-payoff and total-payoff through windows}}, doi = {10.1007/978-3-319-02444-8_10}, volume = {8172}, year = {2013}, } @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}, }