@inproceedings{3866, abstract = {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.}, author = {Bloem, Roderick and Chatterjee, Krishnendu and Greimel, Karin and Henzinger, Thomas A and Jobstmann, Barbara}, editor = {Touili, Tayssir and Cook, Byron and Jackson, Paul}, location = {Edinburgh, UK}, pages = {410 -- 424}, publisher = {Springer}, title = {{Robustness in the presence of liveness}}, doi = {10.1007/978-3-642-14295-6_36}, volume = {6174}, year = {2010}, } @article{3867, abstract = {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.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A}, journal = {Logical Methods in Computer Science}, number = {3}, pages = {1 -- 23}, publisher = {International Federation of Computational Logic}, title = {{Expressiveness and closure properties for quantitative languages}}, doi = {10.2168/LMCS-6(3:10)2010}, volume = {6}, year = {2010}, } @article{3868, abstract = {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}, author = {Chatterjee, Krishnendu and De Alfaro, Luca and Majumdar, Ritankar and Raman, Vishwanath}, journal = {Logical Methods in Computer Science}, number = {3}, pages = {1 -- 27}, publisher = {International Federation of Computational Logic}, title = {{Algorithms for game metrics}}, doi = {10.2168/LMCS-6(3:13)2010}, volume = {6}, year = {2010}, } @inproceedings{4388, abstract = {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.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Jobstmann, Barbara and Radhakrishna, Arjun}, location = {Edinburgh, UK}, pages = {665 -- 669}, publisher = {Springer}, title = {{GIST: A solver for probabilistic games}}, doi = {10.1007/978-3-642-14295-6_57}, volume = {6174}, year = {2010}, } @inproceedings{4569, abstract = {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.}, author = {Bloem, Roderick and Chatterjee, Krishnendu and Henzinger, Thomas A and Jobstmann, Barbara}, location = {Grenoble, France}, pages = {140 -- 156}, publisher = {Springer}, title = {{Better quality in synthesis through quantitative objectives}}, doi = {10.1007/978-3-642-02658-4_14}, volume = {5643}, year = {2009}, } @misc{5392, abstract = {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.}, author = {Chatterjee, Krishnendu}, issn = {2664-1690}, pages = {17}, publisher = {IST Austria}, title = {{Probabilistic automata on infinite words: Decidability and undecidability results}}, doi = {10.15479/AT:IST-2009-0004}, year = {2009}, } @misc{5393, abstract = {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.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Jobstmann, Barbara and Radhakrishna, Arjun}, issn = {2664-1690}, pages = {12}, publisher = {IST Austria}, title = {{Gist: A solver for probabilistic games}}, doi = {10.15479/AT:IST-2009-0003}, year = {2009}, } @misc{5394, abstract = {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.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Horn, Florian}, issn = {2664-1690}, pages = {11}, publisher = {IST Austria}, title = {{Improved lower bounds for request-response and finitary Streett games}}, doi = {10.15479/AT:IST-2009-0002}, year = {2009}, } @misc{5395, abstract = {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.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A}, issn = {2664-1690}, pages = {20}, publisher = {IST Austria}, title = {{Qualitative analysis of partially-observable Markov decision processes}}, doi = {10.15479/AT:IST-2009-0001}, year = {2009}, } @article{3870, abstract = {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.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Horn, Florian}, journal = {ACM Transactions on Computational Logic (TOCL)}, number = {1}, publisher = {ACM}, title = {{Finitary winning in omega-regular games}}, doi = {10.1145/1614431.1614432}, volume = {11}, year = {2009}, } @inproceedings{3871, abstract = {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.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A}, location = {Bologna, Italy}, pages = {244 -- 258}, publisher = {Springer}, title = {{Probabilistic weighted automata}}, doi = {10.1007/978-3-642-04081-8_17}, volume = {5710}, year = {2009}, } @inproceedings{4542, abstract = {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.}, author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A}, location = {Wroclaw, Poland}, pages = {3 -- 13}, publisher = {Springer}, title = {{Alternating weighted automata}}, doi = {10.1007/978-3-642-03409-1_2}, volume = {5699}, year = {2009}, } @inproceedings{4543, abstract = {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.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Horn, Florian}, location = {High Tatras, Slovakia}, pages = {34 -- 54}, publisher = {Springer}, title = {{Stochastic games with finitary objectives}}, doi = {10.1007/978-3-642-03816-7_4}, volume = {5734}, year = {2009}, } @inproceedings{4545, abstract = {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. }, author = {Chatterjee, Krishnendu and Doyen, Laurent and Henzinger, Thomas A}, location = {Rhodos, Greece}, pages = {1 -- 15}, publisher = {Springer}, title = {{A survey of stochastic games with limsup and liminf objectives}}, doi = {10.1007/978-3-642-02930-1_1}, volume = {5556}, year = {2009}, }