TY - CONF
AB - In this paper, we investigate the computational complexity of quantitative information flow (QIF) problems. Information-theoretic quantitative relaxations of noninterference (based on Shannon entropy)have been introduced to enable more fine-grained reasoning about programs in situations where limited information flow is acceptable. The QIF bounding problem asks whether the information flow in a given program is bounded by a constant $d$. Our first result is that the QIF bounding problem is PSPACE-complete. The QIF memoryless synthesis problem asks whether it is possible to resolve nondeterministic choices in a given partial program in such a way that in the resulting deterministic program, the quantitative information flow is bounded by a given constant $d$. Our second result is that the QIF memoryless synthesis problem is also EXPTIME-complete. The QIF memoryless synthesis problem generalizes to QIF general synthesis problem which does not impose the memoryless requirement (that is, by allowing the synthesized program to have more variables then the original partial program). Our third result is that the QIF general synthesis problem is EXPTIME-hard.
AU - Cerny, Pavol
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
ID - 3361
TI - The complexity of quantitative information flow problems
ER -
TY - GEN
AB - We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, Büchi, coBüchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs for probabilistic finite automata and present a complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Tracol, Mathieu
ID - 3363
TI - The decidability frontier for probabilistic automata on infinite words
ER -
TY - CONF
AB - We present the tool Quasy, a quantitative synthesis tool. Quasy takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. The user can choose between a system that satisfies and optimizes the specifications (a) under all possible environment behaviors or (b) under the most-likely environment behaviors given as a probability distribution on the possible input sequences. Quasy solves these two quantitative synthesis problems by reduction to instances of 2-player games and Markov Decision Processes (MDPs) with quantitative winning objectives. Quasy can also be seen as a game solver for quantitative games. Most notable, it can solve lexicographic mean-payoff games with 2 players, MDPs with mean-payoff objectives, and ergodic MDPs with mean-payoff parity objectives.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
AU - Singh, Rohit
ID - 3365
TI - QUASY: quantitative synthesis tool
VL - 6605
ER -
TY - CONF
AB - We present an algorithmic method for the quantitative, performance-aware synthesis of concurrent programs. The input consists of a nondeterministic partial program and of a parametric performance model. The nondeterminism allows the programmer to omit which (if any) synchronization construct is used at a particular program location. The performance model, specified as a weighted automaton, can capture system architectures by assigning different costs to actions such as locking, context switching, and memory and cache accesses. The quantitative synthesis problem is to automatically resolve the nondeterminism of the partial program so that both correctness is guaranteed and performance is optimal. As is standard for shared memory concurrency, correctness is formalized "specification free", in particular as race freedom or deadlock freedom. For worst-case (average-case) performance, we show that the problem can be reduced to 2-player graph games (with probabilistic transitions) with quantitative objectives. While we show, using game-theoretic methods, that the synthesis problem is Nexp-complete, we present an algorithmic method and an implementation that works efficiently for concurrent programs and performance models of practical interest. We have implemented a prototype tool and used it to synthesize finite-state concurrent programs that exhibit different programming patterns, for several performance models representing different architectures.
AU - Cerny, Pavol
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
AU - Singh, Rohit
ED - Gopalakrishnan, Ganesh
ED - Qadeer, Shaz
ID - 3366
TI - Quantitative synthesis for concurrent programs
VL - 6806
ER -
TY - CONF
AB - GIST is a tool that (a) solves the qualitative analysis problem of turn-based probabilistic games with ω-regular objectives; and (b) synthesizes reasonable environment assumptions for synthesis of unrealizable specifications. Our tool provides the first and efficient implementations of several reduction-based techniques to solve turn-based probabilistic games, and uses the analysis of turn-based probabilistic games for synthesizing environment assumptions for unrealizable specifications.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
AU - Radhakrishna, Arjun
ID - 4388
TI - GIST: A solver for probabilistic games
VL - 6174
ER -
TY - CONF
AB - Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system depends on the decisions of both players, supplemented by chance. In this work, we focus on the notion of randomised strategy. More specifically, we show that three natural definitions may lead to very different results: in the most general cases, an almost-surely winning situation may become almost-surely losing if the player is only allowed to use a weaker notion of strategy. In more reasonable settings, translations exist, but they require infinite memory, even in simple cases. Finally, some traditional problems becomes undecidable for the strongest type of strategies.
AU - Cristau, Julien
AU - David, Claire
AU - Horn, Florian
ID - 489
T2 - Proceedings of GandALF 2010
TI - How do we remember the past in randomised strategies?
VL - 25
ER -
TY - GEN
AB - We present an algorithmic method for the synthesis of concurrent programs that are optimal with respect to quantitative performance measures. The input consists of a sequential sketch, that is, a program that does not contain synchronization constructs, and of a parametric performance model that assigns costs to actions such as locking, context switching, and idling. The quantitative synthesis problem is to automatically introduce synchronization constructs into the sequential sketch so that both correctness is guaranteed and worst-case (or average-case) performance is optimized. Correctness is formalized as race freedom or linearizability.
We show that for worst-case performance, the problem can be modeled
as a 2-player graph game with quantitative (limit-average) objectives, and
for average-case performance, as a 2 1/2 -player graph game (with probabilistic transitions). In both cases, the optimal correct program is derived from an optimal strategy in the corresponding quantitative game. We prove that the respective game problems are computationally expensive (NP-complete), and present several techniques that overcome the theoretical difficulty in cases of concurrent programs of practical interest.
We have implemented a prototype tool and used it for the automatic syn- thesis of programs that access a concurrent list. For certain parameter val- ues, our method automatically synthesizes various classical synchronization schemes for implementing a concurrent list, such as fine-grained locking or a lazy algorithm. For other parameter values, a new, hybrid synchronization style is synthesized, which uses both the lazy approach and coarse-grained locks (instead of standard fine-grained locks). The trade-off occurs because while fine-grained locking tends to decrease the cost that is due to waiting for locks, it increases cache size requirements.
AU - Chatterjee, Krishnendu
AU - Cerny, Pavol
AU - Henzinger, Thomas A
AU - Radhakrishna, Arjun
AU - Singh, Rohit
ID - 5388
SN - 2664-1690
TI - Quantitative synthesis for concurrent programs
ER -
TY - GEN
AB - The class of ω regular languages provide a robust specification language in verification. Every ω-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens “eventually.” Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider the finitary parity and Streett (fairness) conditions. We present the topological, automata-theoretic and logical characterization of finitary languages defined by finitary parity and Streett conditions. We (a) show that the finitary parity and Streett languages are Σ2-complete; (b) present a complete characterization of the expressive power of various classes of automata with finitary and infinitary conditions (in particular we show that non-deterministic finitary parity and Streett automata cannot be determinized to deterministic finitary parity or Streett automata); and (c) show that the languages defined by non-deterministic finitary parity automata exactly characterize the star-free fragment of ωB-regular languages.
AU - Chatterjee, Krishnendu
AU - Fijalkow, Nathanaël
ID - 5390
SN - 2664-1690
TI - Topological, automata-theoretic and logical characterization of finitary languages
ER -
TY - CONF
AB - 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 objective. 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 polynomially 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.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 3851
TI - Energy parity games
VL - 6199
ER -
TY - CONF
AB - We introduce two-level discounted games played by two players on a perfect-information stochastic game graph. The upper level game is a discounted game and the lower level game is an undiscounted reachability game. Two-level games model hierarchical and sequential decision making under uncertainty across different time scales. We show the existence of pure memoryless optimal strategies for both players and an ordered field property for such games. 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 games can be decided in NP intersected coNP. We also give an alternate strategy improvement algorithm to compute the value.
AU - Chatterjee, Krishnendu
AU - Majumdar, Ritankar
ID - 3852
TI - Discounting in games across time scales
VL - 25
ER -
TY - CONF
AB - Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. When the mode of branching of the automaton is deterministic, nondeterministic, or alternating, the corresponding class of quantitative languages is not robust as it is not closed under the pointwise operations of max, min, sum, and numerical complement. Nondeterministic and alternating mean-payoff automata are not decidable either, as the quantitative generalization of the problems of universality and language inclusion is undecidable. We introduce a new class of quantitative languages, defined by mean-payoff automaton expressions, which is robust and decidable: it is closed under the four pointwise operations, and we show that all decision problems are decidable for this class. Mean-payoff automaton expressions subsume deterministic meanpayoff automata, and we show that they have expressive power incomparable to nondeterministic and alternating mean-payoff automata. We also present for the first time an algorithm to compute distance between two quantitative languages, and in our case the quantitative languages are given as mean-payoff automaton expressions.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Edelsbrunner, Herbert
AU - Henzinger, Thomas A
AU - Rannou, Philippe
ID - 3853
TI - Mean-payoff automaton expressions
VL - 6269
ER -
TY - CONF
AB - Graph games of infinite length provide a natural model for open reactive systems: one player (Eve) represents the controller and the other player (Adam) represents the environment. The evolution of the system depends on the decisions of both players. The specification for the system is usually given as an ω-regular language L over paths and Eve’s goal is to ensure that the play belongs to L irrespective of Adam’s behaviour. The classical notion of winning strategies fails to capture several interesting scenarios. For example, strong fairness (Streett) conditions are specified by a number of request-grant pairs and require every pair that is requested infinitely often to be granted infinitely often: Eve might win just by preventing Adam from making any new request, but a “better” strategy would allow Adam to make as many requests as possible and still ensure fairness. To address such questions, we introduce the notion of obliging games, where Eve has to ensure a strong condition Φ, while always allowing Adam to satisfy a weak condition Ψ. We present a linear time reduction of obliging games with two Muller conditions Φ and Ψ to classical Muller games. We consider obliging Streett games and show they are co-NP complete, and show a natural quantitative optimisation problem for obliging Streett games is in FNP. We also show how obliging games can provide new and interesting semantics for multi-player games.
AU - Chatterjee, Krishnendu
AU - Horn, Florian
AU - Löding, Christof
ID - 3854
TI - Obliging games
VL - 6269
ER -
TY - CONF
AB - We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with parity objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider qualitative analysis problems: given a POMDP with a parity objective, decide whether there exists an observation-based strategy to achieve the objective with probability 1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis problem for POMDPs with parity objectives and its subclasses: safety, reachability, Büchi, and coBüchi objectives. We establish several upper and lower bounds that were not known in the literature. Second, we give optimal bounds (matching upper and lower bounds) for the memory required by pure and randomized observation-based strategies for each class of objectives.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3855
TI - Qualitative analysis of partially-observable Markov Decision Processes
VL - 6281
ER -
TY - CONF
AB - We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (players interact simultaneously); and (b) turn-based (players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. We present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function (probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Henzinger, Thomas A
ID - 3856
TI - Randomness for free
VL - 6281
ER -
TY - CONF
AB - We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, Büchi, coBüchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs for probabilistic finite automata and present an almost complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
ID - 3857
TI - Probabilistic Automata on infinite words: decidability and undecidability results
VL - 6252
ER -
TY - CONF
AB - We consider two-player zero-sum games on graphs. On the basis of the information available to the players 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 com- plete view of the game). We survey the complexity results for the problem of de- ciding the winner in various classes of partial-observation games with ω-regular winning conditions specified as parity objectives. We present a reduction from the class of parity objectives that depend on sequence of states of the game to the sub-class of parity objectives that only depend on the sequence of observations. We also establish that partial-observation acyclic games are PSPACE-complete.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
ID - 3858
TI - The complexity of partial-observation parity games
VL - 6397
ER -
TY - GEN
AB - This book constitutes the proceedings of the 8th International Conference on Formal Modeling and Analysis of Timed Systems, FORMATS 2010, held in Klosterneuburg, Austria in September 2010. The 14 papers presented were carefully reviewed and selected from 31 submissions. In addition, the volume contains 3 invited talks and 2 invited tutorials.The aim of FORMATS is to promote the study of fundamental and practical aspects of timed systems, and to bring together researchers from different disciplines that share an interest in the modeling and analysis of timed systems. Typical topics include foundations and semantics, methods and tools, and applications.
ED - Chatterjee, Krishnendu
ED - Henzinger, Thomas A
ID - 3859
TI - Formal modeling and analysis of timed systems
VL - 6246
ER -
TY - CONF
AB - In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Generalized mean-payoff and energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be (resp. remain) nonnegative. These games have applications in the synthesis of resource-bounded processes with multiple resources. We prove the finite-memory determinacy of generalized energy games and show the inter- reducibility of generalized mean-payoff and energy games for finite-memory strategies. We also improve the computational complexity for solving both classes of games with finite-memory strategies: while the previously best known upper bound was EXPSPACE, and no lower bound was known, we give an optimal coNP-complete bound. For memoryless strategies, we show that the problem of deciding the existence of a winning strategy for the protagonist is NP-complete.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
AU - Raskin, Jean
ID - 3860
TI - Generalized mean-payoff and energy games
VL - 8
ER -
TY - JOUR
AB - We introduce strategy logic, a logic that treats strategies in two-player games as explicit first-order objects. The explicit treatment of strategies allows us to specify properties of nonzero-sum games in a simple and natural way. We show that the one-alternation fragment of strategy logic is strong enough to express the existence of Nash equilibria and secure equilibria, and subsumes other logics that were introduced to reason about games, such as ATL, ATL*, and game logic. We show that strategy logic is decidable, by constructing tree automata that recognize sets of strategies. While for the general logic, our decision procedure is nonelementary, for the simple fragment that is used above we show that the complexity is polynomial in the size of the game graph and optimal in the size of the formula (ranging from polynomial to 2EXPTIME depending on the form of the formula).
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Piterman, Nir
ID - 3861
IS - 6
JF - Information and Computation
TI - Strategy logic
VL - 208
ER -
TY - JOUR
AB - We consider two-player parity games with imperfect information in which strategies rely on observations that provide imperfect information about the history of a play. To solve such games, i.e., to determine the winning regions of players and corresponding winning strategies, one can use the subset construction to build an equivalent perfect-information game. Recently, an algorithm that avoids the inefficient subset construction has been proposed. The algorithm performs a fixed-point computation in a lattice of antichains, thus maintaining a succinct representation of state sets. However, this representation does not allow to recover winning strategies. In this paper, we build on the antichain approach to develop an algorithm for constructing the winning strategies in parity games of imperfect information. One major obstacle in adapting the classical procedure is that the complementation of attractor sets would break the invariant of downward-closedness on which the antichain representation relies. We overcome this difficulty by decomposing problem instances recursively into games with a combination of reachability, safety, and simpler parity conditions. We also report on an experimental implementation of our algorithm: to our knowledge, this is the first implementation of a procedure for solving imperfect-information parity games on graphs.
AU - Berwanger, Dietmar
AU - Chatterjee, Krishnendu
AU - De Wulf, Martin
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3863
IS - 10
JF - Information and Computation
TI - Strategy construction for parity games with imperfect information
VL - 208
ER -
TY - CONF
AB - Often one has a preference order among the different systems that satisfy a given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimal-synthesis problem: given an omega-regular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification tinder the given input assumption, synthesize a system that optimizes the measured value. For safety specifications and measures that are defined by mean-payoff automata, the optimal-synthesis problem amounts to finding a strategy in a Markov decision process (MDP) that is optimal for a long-run average reward objective, which can be done in polynomial time. For general omega-regular specifications, the solution rests on a new, polynomial-time algorithm for computing optimal strategies in MDPs with mean-payoff parity objectives. We present some experimental results showing optimal systems that were automatically generated in this way.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
AU - Singh, Rohit
ID - 3864
TI - Measuring and synthesizing systems in probabilistic environments
VL - 6174
ER -
TY - CONF
AB - We introduce a technique for debugging multi-threaded C programs and analyzing the impact of source code changes, and its implementation in the prototype tool DIRECT. Our approach uses a combination of source code instrumentation and runtime management. The source code along with a test harness is instrumented to monitor Operating System (OS) and user defined function calls. DIRECT tracks all concurrency control primitives and, optionally, data from the program. DIRECT maintains an abstract global state that combines information from every thread, including the sequence of function calls and concurrency primitives executed. The runtime manager can insert delays, provoking thread inter-leavings that may exhibit bugs that are difficult to reach otherwise. The runtime manager collects an approximation of the reachable state space and uses this approximation to assess the impact of change in a new version of the program.
AU - Chatterjee, Krishnendu
AU - De Alfaro, Luca
AU - Raman, Vishwanath
AU - Sánchez, César
ED - Rosenblum, David
ED - Taenzer, Gabriele
ID - 3865
TI - Analyzing the impact of change in multi-threaded programs
VL - 6013
ER -
TY - CONF
AB - Systems ought to behave reasonably even in circumstances that are not anticipated in their specifications. We propose a definition of robustness for liveness specifications which prescribes, for any number of environment assumptions that are violated, a minimal number of system guarantees that must still be fulfilled. This notion of robustness can be formulated and realized using a Generalized Reactivity formula. We present an algorithm for synthesizing robust systems from such formulas. For the important special case of Generalized Reactivity formulas of rank 1, our algorithm improves the complexity of [PPS06] for large specifications with a small number of assumptions and guarantees.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Greimel, Karin
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
ED - Touili, Tayssir
ED - Cook, Byron
ED - Jackson, Paul
ID - 3866
TI - Robustness in the presence of liveness
VL - 6174
ER -
TY - JOUR
AB - Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages L that assign to each word w a real number L(w). In the case of infinite words, the value of a run is naturally computed as the maximum, limsup, liminf, limit-average, or discounted-sum of the transition weights. The value of a word w is the supremum of the values of the runs over w. We study expressiveness and closure questions about these quantitative languages. We first show that the set of words with value greater than a threshold can be omega-regular for deterministic limit-average and discounted-sum automata, while this set is always omega-regular when the threshold is isolated (i.e., some neighborhood around the threshold contains no word). In the latter case, we prove that the omega-regular language is robust against small perturbations of the transition weights. We next consider automata with transition weights 0 or 1 and show that they are as expressive as general weighted automata in the limit-average case, but not in the discounted-sum case. Third, for quantitative languages L-1 and L-2, we consider the operations max(L-1, L-2), min(L-1, L-2), and 1 - L-1, which generalize the boolean operations on languages, as well as the sum L-1 + L-2. We establish the closure properties of all classes of quantitative languages with respect to these four operations.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3867
IS - 3
JF - Logical Methods in Computer Science
TI - Expressiveness and closure properties for quantitative languages
VL - 6
ER -
TY - JOUR
AB - Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative mu-calculus and related probabilistic logics. We first show that the metrics provide a bound for the difference in long-run average and discounted average behavior across states, indicating that the metrics can be used both in system verification, and in performance evaluation. For turn-based games and MDPs, we provide a polynomial-time algorithm for the computation of the one-step metric distance between states. The algorithm is based on linear programming; it improves on the previous known exponential-time algorithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the best known algorithms for Markov chains. For the bisimulation kernel of the metric our algorithm works in time O(n(4)) for both turn-based games and MDPs; improving the previously best known O(n(9).log(n)) time algorithm for MDPs. For a concurrent game G, we show that computing the exact distance be tween states is at least as hard as computing the value of concurrent reachability games and the square-root-sum problem in computational geometry. We show that checking whether the metric distance is bounded by a rational r, can be done via a reduction to the theory of real closed fields, involving a formula with three quantifier alternations, yielding O(vertical bar G vertical bar(O(vertical bar G vertical bar 5))) time complexity, improving the previously known reduction, which yielded O(vertical bar G vertical bar(O(vertical bar G vertical bar 7))) time complexity. These algorithms can be iterated to approximate the metrics using binary search
AU - Chatterjee, Krishnendu
AU - De Alfaro, Luca
AU - Majumdar, Ritankar
AU - Raman, Vishwanath
ID - 3868
IS - 3
JF - Logical Methods in Computer Science
TI - Algorithms for game metrics
VL - 6
ER -
TY - CONF
AB - Weighted automata are finite automata with numerical weights on transitions. Nondeterministic weighted automata define quantitative languages L that assign to each word w a real number L(w) computed as the maximal value of all runs over w, and the value of a run r is a function of the sequence of weights that appear along r. There are several natural functions to consider such as Sup, LimSup, LimInf, limit average, and discounted sum of transition weights.
We introduce alternating weighted automata in which the transitions of the runs are chosen by two players in a turn-based fashion. Each word is assigned the maximal value of a run that the first player can enforce regardless of the choices made by the second player. We survey the results about closure properties, expressiveness, and decision problems for nondeterministic weighted automata, and we extend these results to alternating weighted automata.
For quantitative languages L 1 and L 2, we consider the pointwise operations max(L 1,L 2), min(L 1,L 2), 1 − L 1, and the sum L 1 + L 2. We establish the closure properties of all classes of alternating weighted automata with respect to these four operations.
We next compare the expressive power of the various classes of alternating and nondeterministic weighted automata over infinite words. In particular, for limit average and discounted sum, we show that alternation brings more expressive power than nondeterminism.
Finally, we present decidability results and open questions for the quantitative extension of the classical decision problems in automata theory: emptiness, universality, language inclusion, and language equivalence.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 4542
TI - Alternating weighted automata
VL - 5699
ER -
TY - CONF
AB - The synthesis of a reactive system with respect to all omega-regular specification requires the solution of a graph game. Such games have been extended in two natural ways. First, a game graph can be equipped with probabilistic choices between alternative transitions, thus allowing the, modeling of uncertain behaviour. These are called stochastic games. Second, a liveness specification can he strengthened to require satisfaction within all unknown but bounded amount of time. These are called finitary objectives. We study. for the first time, the, combination of Stochastic games and finitary objectives. We characterize the requirements on optimal strategies and provide algorithms for Computing the maximal achievable probability of winning stochastic games with finitary parity or Street, objectives. Most notably the set of state's from which a player can win with probability . for a finitary parity objective can he computed in polynomial time even though no polynomial-time algorithm is known in the nonfinitary case.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Horn, Florian
ID - 4543
TI - Stochastic games with finitary objectives
VL - 5734
ER -
TY - CONF
AB - A stochastic game is a two-player game played oil a graph, where in each state the successor is chosen either by One of the players, or according to a probability distribution. We Survey Stochastic games with limsup and liminf objectives. A real-valued re-ward is assigned to each state, and the value of all infinite path is the limsup (resp. liminf) of all rewards along the path. The value of a stochastic game is the maximal expected value of an infinite path that call he achieved by resolving the decisions of the first player. We present the complexity of computing values of Stochastic games and their subclasses, and the complexity, of optimal strategies in such games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 4545
TI - A survey of stochastic games with limsup and liminf objectives
VL - 5556
ER -
TY - CONF
AB - Most specification languages express only qualitative constraints. However, among two implementations that satisfy a given specification, one may be preferred to another. For example, if a specification asks that every request is followed by a response, one may prefer an implementation that generates responses quickly but does not generate unnecessary responses. We use quantitative properties to measure the “goodness” of an implementation. Using games with corresponding quantitative objectives, we can synthesize “optimal” implementations, which are preferred among the set of possible implementations that satisfy a given specification.
In particular, we show how automata with lexicographic mean-payoff conditions can be used to express many interesting quantitative properties for reactive systems. In this framework, the synthesis of optimal implementations requires the solution of lexicographic mean-payoff games (for safety requirements), and the solution of games with both lexicographic mean-payoff and parity objectives (for liveness requirements). We present algorithms for solving both kinds of novel graph games.
AU - Bloem, Roderick
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
ID - 4569
TI - Better quality in synthesis through quantitative objectives
VL - 5643
ER -
TY - GEN
AB - We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, Büchi, coBüchi and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs of [GO09] and present a precise characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems.
AU - Chatterjee, Krishnendu
ID - 5392
SN - 2664-1690
TI - Probabilistic automata on infinite words: Decidability and undecidability results
ER -
TY - GEN
AB - Gist is a tool that (a) solves the qualitative analysis problem of turn-based probabilistic games with ω-regular objectives; and (b) synthesizes reasonable environment assumptions for synthesis of unrealizable specifications. Our tool provides efficient implementations of several reduction based techniques to solve turn-based probabilistic games, and uses the analysis of turn-based probabilistic games for synthesizing environment assumptions for unrealizable specifications.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Jobstmann, Barbara
AU - Radhakrishna, Arjun
ID - 5393
SN - 2664-1690
TI - Gist: A solver for probabilistic games
ER -
TY - GEN
AB - We consider two-player games played on graphs with request-response and finitary Streett objectives. We show these games are PSPACE-hard, improving the previous known NP-hardness. We also improve the lower bounds on memory required by the winning strategies for the players.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Horn, Florian
ID - 5394
SN - 2664-1690
TI - Improved lower bounds for request-response and finitary Streett games
ER -
TY - GEN
AB - We study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observa- tions. We consider the qualitative analysis problem: given a POMDP with an omega-regular objective, whether there is an observation-based strategy to achieve the objective with probability 1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis of POMDPs with parity objectives (a canonical form to express omega-regular objectives) and its subclasses. Our contribution consists in establishing several upper and lower bounds that were not known in literature. Second, we present optimal bounds (matching upper and lower bounds) on the memory required by pure and randomized observation-based strategies for the qualitative analysis of POMDPs with parity objectives and its subclasses.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 5395
SN - 2664-1690
TI - Qualitative analysis of partially-observable Markov decision processes
ER -
TY - JOUR
AB - Games on graphs with omega-regular objectives provide a model for the control and synthesis of reactive systems. Every omega-regular objective can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens “eventually.” Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. While for one-shot liveness (reachability) objectives, classical and finitary liveness coincide, for repeated liveness (Buchi) objectives, the finitary formulation is strictly stronger. In this work we study games with finitary parity and Streett objectives. We prove the determinacy of these games, present algorithms for solving these games, and characterize the memory requirements of winning strategies. We show that finitary parity games can be solved in polynomial time, which is not known for infinitary parity games. For finitary Streett games, we give an EXPTIME algorithm and show that the problem is NP-hard. Our algorithms can be used, for example, for synthesizing controllers that do not let the response time of a system increase without bound.
AU - Chatterjee, Krishnendu
AU - Henzinger, Thomas A
AU - Horn, Florian
ID - 3870
IS - 1
JF - ACM Transactions on Computational Logic (TOCL)
TI - Finitary winning in omega-regular games
VL - 11
ER -
TY - CONF
AB - Nondeterministic weighted automata are finite automata with numerical weights oil transitions. They define quantitative languages 1, that assign to each word v; a real number L(w). The value of ail infinite word w is computed as the maximal value of all runs over w, and the value of a run as the supremum, limsup liminf, limit average, or discounted sum of the transition weights. We introduce probabilistic weighted antomata, in which the transitions are chosen in a randomized (rather than nondeterministic) fashion. Under almost-sure semantics (resp. positive semantics), the value of a word v) is the largest real v such that the runs over w have value at least v with probability I (resp. positive probability). We study the classical questions of automata theory for probabilistic weighted automata: emptiness and universality, expressiveness, and closure under various operations oil languages. For quantitative languages, emptiness university axe defined as whether the value of some (resp. every) word exceeds a given threshold. We prove some, of these questions to he decidable, and others undecidable. Regarding expressive power, we show that probabilities allow its to define a wide variety of new classes of quantitative languages except for discounted-sum automata, where probabilistic choice is no more expressive than nondeterminism. Finally we live ail almost complete picture of the closure of various classes of probabilistic weighted automata for the following, provide, is operations oil quantitative languages: maximum, sum. and numerical complement.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
ID - 3871
TI - Probabilistic weighted automata
VL - 5710
ER -