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 - 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 - 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 -