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13
Qualitative Determinacy and Decidability of Stochastic Games with Signals
, 2009
"... We consider the standard model of finite twoperson zerosum stochastic games with signals. We are interested in the existence of almostsurely winning or positively winning strategies, under reachability, safety, Büchi or coBüchi winning objectives. We prove two qualitative determinacy results. Fi ..."
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Cited by 17 (4 self)
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We consider the standard model of finite twoperson zerosum stochastic games with signals. We are interested in the existence of almostsurely winning or positively winning strategies, under reachability, safety, Büchi or coBüchi winning objectives. We prove two qualitative determinacy results. First, in a reachability game either player 1 can achieve almostsurely the reachability objective, or player 2 can ensure surely the complementary safety objective, or both players have positively winning strategies. Second, in a Büchi game if player 1 cannot achieve almostsurely the Büchi objective, then player 2 can ensure positively the complementary coBüchi objective. We prove that players only need strategies with finitememory, whose sizes range from no memory at all to doublyexponential number of states, with matching lower bounds. Together with the qualitative determinacy results, we also provide fixpoint algorithms for deciding which player has an almostsurely winning or a positively winning strategy and for computing the finite memory strategy. Complexity ranges from EXPTIME to 2EXPTIME with matching lower bounds, and better complexity can be achieved for some special cases where one of the players is better informed than her opponent.
Qualitative analysis of partiallyobservable Markov decision processes
 In CoRR: 0909.1645
, 2009
"... Abstract. We study observationbased strategies for partiallyobservable Markov decision processes (POMDPs) with omegaregular objectives. An observationbased strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider the qualitative ..."
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Abstract. We study observationbased strategies for partiallyobservable Markov decision processes (POMDPs) with omegaregular objectives. An observationbased strategy relies on partial information about the history of a play, namely, on the past sequence of observations. We consider the qualitative analysis problem: given a POMDP with an omegaregular objective, whether there is an observationbased strategy to achieve the objective with probability 1 (almostsure 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 omegaregular 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 observationbased strategies for the qualitative analysis of POMDPs with parity objectives and its subclasses. 1
Qualitative Concurrent Stochastic Games with Imperfect Information
, 2009
"... We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor state is chosen accordingly to some fixed probability dist ..."
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Cited by 7 (1 self)
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We study a model of games that combines concurrency, imperfect information and stochastic aspects. Those are finite states games in which, at each round, the two players choose, simultaneously and independently, an action. Then a successor state is chosen accordingly to some fixed probability distribution depending on the previous state and on the pair of actions chosen by the players. Imperfect information is modeled as follows: both players have an equivalence relation over states and, instead of observing the exact state, they only know to which equivalence class it belongs. Therefore, if two partial plays are indistinguishable by some player, he should behave the same in both of them. We consider reachability (does the play eventually visit a final state?) and Büchi objective (does the play visit infinitely often a final state?). Our main contribution is to prove that the following problem is complete for 2ExpTime: decide whether the first player has a strategy that ensures her to almostsurely win against any possible strategy of her oponent. We also characterise those strategies needed by the first player to almostsurely win.
Alpaga: A Tool for Solving Parity Games with Imperfect Information, in
 Proc. of TACAS 2009, LNCS 5505
"... Abstract. Alpaga is a solver for twoplayer parity games with imperfect information. Given the description of a game, it determines whether the first player can ensure to win and, if so, it constructs a winning strategy. The tool provides a symbolic implementation of a recent algorithm based on anti ..."
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Abstract. Alpaga is a solver for twoplayer parity games with imperfect information. Given the description of a game, it determines whether the first player can ensure to win and, if so, it constructs a winning strategy. The tool provides a symbolic implementation of a recent algorithm based on antichains. 1
Antichain Algorithms for Finite Automata
"... We present a general theory that exploits simulation relations on transition systems to obtain antichain algorithms for solving the reachability and repeated reachability problems. Antichains are more succinct than the sets of states manipulated by the traditional fixpoint algorithms. The theory ju ..."
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We present a general theory that exploits simulation relations on transition systems to obtain antichain algorithms for solving the reachability and repeated reachability problems. Antichains are more succinct than the sets of states manipulated by the traditional fixpoint algorithms. The theory justifies the correctness of the antichain algorithms, and applications such as the universality problem for finite automata illustrate efficiency improvements. Finally, we show that new and provably better antichain algorithms can be obtained for the emptiness problem of alternating automata over finite and infinite words.
Games with Imperfect Information: Theory and Algorithms ⋆
"... Abstract. We study observationbased strategies for twoplayer turnbased games played on graphs with parity objectives. An observationbased strategy relies on imperfect information about the history of a play, namely, on the past sequence of observations. Such games occur in the synthesis of a contr ..."
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Cited by 3 (1 self)
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Abstract. We study observationbased strategies for twoplayer turnbased games played on graphs with parity objectives. An observationbased strategy relies on imperfect information about the history of a play, namely, on the past sequence of observations. Such games occur in the synthesis of a controller that does not see the private state of the plant. Our main results are twofold. First, we give a fixedpoint algorithm for computing the set of states from which a player can win with a deterministic observationbased strategy. Second, we give an algorithm for computing the set of states from which a player can win with probability 1 with a randomized observationbased strategy for a reachability objective. This set is of interest because in the absence of perfect information, randomized strategies are more powerful than deterministic ones. 1
• Lubo˘s Brim
"... • Igor Walukiewicz (reviewer) iiiAcknowledgments The work presented in this manuscript has been carried out in the group of Tom Henzinger at École Polytechnique Fédérale de Lausanne (Oct. 2006 Dec. 2008), in the group of JeanFrançois Raskin at Université Libre de Bruxelles (Jan. 2009Sep. 2009), a ..."
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• Igor Walukiewicz (reviewer) iiiAcknowledgments The work presented in this manuscript has been carried out in the group of Tom Henzinger at École Polytechnique Fédérale de Lausanne (Oct. 2006 Dec. 2008), in the group of JeanFrançois Raskin at Université Libre de Bruxelles (Jan. 2009Sep. 2009), and in the Laboratoire Spécification et Vérification at ENS Cachan under the auspices of Alain Finkel (since Oct. 2009). Great collaboration with Krishnendu Chatterjee has also been possible through several visits to IST Austria. I would like to warmly thank Tom, JeanFrançois, Alain, and Krishnendu, as well as all my other coauthors:
Emptiness Of Alternating Parity Tree Automata Using Games With Imperfect Information
, 2012
"... Abstract: We focus on the emptiness problem for alternating parity tree automata. The usual technique to tackle this problem first removes alternation, going to nondeterminism, and then checks emptiness by reduction to a twoplayer perfectinformation parity game. In this note, we give an alternati ..."
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Abstract: We focus on the emptiness problem for alternating parity tree automata. The usual technique to tackle this problem first removes alternation, going to nondeterminism, and then checks emptiness by reduction to a twoplayer perfectinformation parity game. In this note, we give an alternative roadmap to this problem by providing a direct reduction to the emptiness problem to solving an imperfectinformation twoplayer parity game. Keywords: Alternating Tree Automata; Emptiness; Imperfect Information Games; Positional Determinacy Le problème du vide pour les automates d’arbres alternant à parité via des jeux à information imparfaite Résumé: Nous considérons le problème du test du vide pour les automates d’arbres alternants à parité. La méthode usuelle pour résoudre ce problème, commence par supprimer l’alternance ce qui conduit à un automate nondéterministe dont le vide est ensuite testé par réduction à un jeux de parité à information parfaite. Dans cette note, nous proposons une approche alternative pour ce problème, en proposant une réduction directe du problème du vide à un jeu de parité à information imparfaite. Mots clés: Automates d’arbres alternants; test du vide; jeux à information imparfaite; déterminaison positionnelle