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14
Pushdown Module Checking with Imperfect Information
, 2012
"... The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems ( ..."
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Cited by 23 (14 self)
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The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems (pushdown module checking). In this paper, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the system’s control states and pushdown store content. We study the complexity of this problem with respect to the branchingtime temporal logics CTL, CTL ∗ and the propositional µcalculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information.
Randomness for free
 CoRR
"... Abstract. We consider twoplayer zerosum 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) partialobservation (both players have partial view o ..."
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Cited by 14 (13 self)
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Abstract. We consider twoplayer zerosum 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) partialobservation (both players have partial view of the game); (b) onesided completeobservation (one player has complete observation); and (c) completeobservation (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) turnbased (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. 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 8 (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.
Assumeguarantee synthesis
 In Proceedings of TACAS’07
, 2007
"... Abstract. The classical synthesis problem for reactive systems asks, given a proponent process A and an opponent process B, to refine A so that the closedloop system AB satisfies a given specification Φ. The solution of this problem requires the computation of a winning strategy for proponent A i ..."
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Abstract. The classical synthesis problem for reactive systems asks, given a proponent process A and an opponent process B, to refine A so that the closedloop system AB satisfies a given specification Φ. The solution of this problem requires the computation of a winning strategy for proponent A in a game against opponent B. We define and study the cosynthesis problem, where the proponent A consists itself of two independent processes, A = A1A2, with specifications Φ1 and Φ2, and the goal is to refine both A1 and A2 so that A1A2B satisfies Φ1 ∧ Φ2. For example, if the opponent B is a fair scheduler for the two processes A1 and A2, and Φi specifies the requirements of mutual exclusion for Ai (e.g., starvation freedom), then the cosynthesis problem asks for the automatic synthesis of a mutualexclusion protocol. We show that cosynthesis defined classically, with the processes A1 and A2 either collaborating or competing, does not capture desirable solutions. Instead, the proper formulation of cosynthesis is the one where process A1 competes with A2 but not at the price of violating Φ1, and vice versa. We call this assumeguarantee synthesis and show that it can be solved by computing secureequilibrium strategies. In particular, from mutualexclusion requirements the assumeguarantee synthesis algorithm automatically computes Peterson’s protocol. 1
Solving PartialInformation Stochastic Parity Games
"... We study onesided partialinformation 2player concurrent stochastic games with parity objectives. In such a game, one of the players has only partial visibility of the state of the game, while the other player has complete knowledge. In general, such games are known to be undecidable, even for the ..."
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We study onesided partialinformation 2player concurrent stochastic games with parity objectives. In such a game, one of the players has only partial visibility of the state of the game, while the other player has complete knowledge. In general, such games are known to be undecidable, even for the case of a single player (POMDP). These undecidability results depend crucially on player strategies that exploit an infinite amount of memory. However, in many applications of games, one is usually more interested in finding a finitememory strategy. We consider the problem of whether the player with partial information has a finitememory winning strategy when the player with complete information is allowed to use an arbitrary amount of memory. We show that this problem is decidable. 1.
Games with Opacity Condition
"... Abstract. We describe the class of games with opacity condition, as an adequate model for security aspects of computing systems. We study their theoretical properties, relate them to reachability perfect information games and exploit this relation to discuss a search approach with heuristics, based ..."
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Abstract. We describe the class of games with opacity condition, as an adequate model for security aspects of computing systems. We study their theoretical properties, relate them to reachability perfect information games and exploit this relation to discuss a search approach with heuristics, based on the directingword problem in automata theory. 1
Games with imperfect information
"... Games have been extensively studied, either in computer science, mathematics or even economy. Nevertheless, each discipline has its own interest in using this formalism. Computer science for instance is attached to calculability issues. These results have some direct applications in model checking ..."
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Games have been extensively studied, either in computer science, mathematics or even economy. Nevertheless, each discipline has its own interest in using this formalism. Computer science for instance is attached to calculability issues. These results have some direct applications in model checking or compilation. Recently, a new type of game has been introduced: games with imperfect information. They allow the modeling of more sophisticated systems, but bring also new calculability problems. In this document, we introduce a general method to prove the determinacy of any type of game. This method is used several times, and allow us to solve some open problems. This document introduces also several examples of important games stating for important properties. Then, a new type of game unifying the concepts of concurrency and imperfect information is presented. Finally, we discuss of the extension on infinite arenas. 1 ha l0
unknown title
"... The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems ( ..."
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The model checking problem for finitestate open systems (module checking) has been extensively studied in the literature, both in the context of environments with perfect and imperfect information about the system. Recently, the perfect information case has been extended to infinitestate systems (pushdown module checking). In this paper, we extend pushdown module checking to the imperfect information setting; i.e., to the case where the environment has only a partial view of the system’s control states and pushdown store content. We study the complexity of this problem with respect to the branchingtime temporal logics CTL, CTL ∗ and the propositional µcalculus. We show that pushdown module checking, which is by itself harder than pushdown model checking, becomes undecidable when the environment has imperfect information. ✩This work is based on the papers [4] appeared in CONCUR 2007 and [5] appeared in