TY - CONF AB - 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. AU - Chatterjee, Krishnendu AU - Fijalkow, Nathanaël ID - 1374 T2 - 22nd EACSL Annual Conference on Computer Science Logic TI - Infinite-state games with finitary conditions VL - 23 ER - TY - CONF AB - 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. AU - Chatterjee, Krishnendu AU - Forejt, Vojtěch AU - Wojtczak, Dominik ID - 2238 TI - Multi-objective discounted reward verification in graphs and MDPs VL - 8312 ER - TY - GEN AB - 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. ED - Chatterjee, Krishnendu ED - Sgall, Jiri ID - 2292 SN - 978-3-642-40312-5 TI - Mathematical Foundations of Computer Science 2013 VL - 8087 ER - TY - JOUR AB - 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. AU - Godhal, Yashdeep AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A ID - 2299 IS - 5-6 JF - International Journal on Software Tools for Technology Transfer TI - Synthesis of AMBA AHB from formal specification: A case study VL - 15 ER - TY - CONF AB - 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. AU - Chatterjee, Krishnendu AU - Gaiser, Andreas AU - Kretinsky, Jan ID - 2446 TI - Automata with generalized Rabin pairs for probabilistic model checking and LTL synthesis VL - 8044 ER - TY - CONF AB - 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. AU - Chatterjee, Krishnendu AU - Ła̧Cki, Jakub ID - 2444 TI - Faster algorithms for Markov decision processes with low treewidth VL - 8044 ER - TY - JOUR AB - 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. AU - Chatterjee, Krishnendu AU - Alfaro, Luca AU - Majumdar, Ritankar ID - 2814 IS - 2 JF - International Journal of Foundations of Computer Science TI - The complexity of coverage VL - 24 ER - TY - JOUR AB - 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. AU - Novak, Sebastian AU - Chatterjee, Krishnendu AU - Nowak, Martin ID - 2817 JF - Journal of Theoretical Biology TI - Density games VL - 334 ER - TY - CONF AB - 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. AU - Chatterjee, Krishnendu AU - Prabhu, Vinayak ID - 2819 T2 - Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control TI - Quantitative timed simulation functions and refinement metrics for real-time systems VL - 1 ER - TY - JOUR AB - 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. AU - Chatterjee, Krishnendu AU - Prabhu, Vinayak ID - 2824 JF - Information and Computation TI - Synthesis of memory-efficient, clock-memory free, and non-Zeno safety controllers for timed systems VL - 228-229 ER -