Stochastic Games with Lossy Channels

Abdulla, Parosh Aziz; Henda, Noomene Ben; Alfaro, Luca de; Mayr, Richard; Sandberg, Sven

doi:10.1007/978-3-540-78499-9_4

Cited by 17 publications

(18 citation statements)

References 31 publications

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“…It is of course possible to consider 2-player stochastic games on arenas generated by probabilistic LCS's: this question was studied first in [14] and later in [2,19]. We proceed as in Sect.…”

Section: Two-player Stochastic Gamesmentioning

confidence: 99%

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Computable fixpoints in well-structured symbolic model checking

Bertrand

Schnoebelen

2012

Form Methods Syst Des

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We prove a general finite-time convergence theorem for fixpoint expressions over a well-quasi-ordered set. This has immediate applications for the verification of wellstructured systems, where a main issue is the computability of fixpoint expressions, and in particular for game-theoretical properties and probabilistic systems where nesting and alternation of least and greatest fixpoints are common.

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Section: Two-player Stochastic Gamesmentioning

confidence: 99%

“…For WSTS's, a generic computability result for a fragment of the μ-language we consider is briefly mentioned in [63]. Our applications to well-structured transition systems generalize results from [2,5,65,72,73] that rely on more ad-hoc proofs of convergence.…”

Section: Introductionmentioning

confidence: 99%

Computable fixpoints in well-structured symbolic model checking

Bertrand

Schnoebelen

2012

Form Methods Syst Des

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“…3.2 where the asymmetry appears: upward-closed sets have a finite basis (on which one can base algorithms), while downward-closed sets do not. 2 …”

Section: The Question Whether For Semilinear X and Y Postmentioning

confidence: 99%

“…Many variations are possible, motivated by different situations. We refer to [3,41,9,10,2,4] for results on such games.…”

Section: Theorem 83mentioning

confidence: 99%

Lossy Counter Machines Decidability Cheat Sheet

Schnoebelen

2010

Lecture Notes in Computer Science

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Abstract. Lossy counter machines (LCM's) are a variant of Minsky counter machines based on weak (or unreliable) counters in the sense that they can decrease nondeterministically and without notification. This model, introduced by R. Mayr [TCS 297:337-354 (2003)], is not yet very well known, even though it has already proven useful for establishing hardness results. In this paper we survey the basic theory of LCM's and their verification problems, with a focus on the decidability/undecidability divide.

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“…The reason for considering infinite-state games is that many recent works study various algorithmic problems for games over classical automata-theoretic models, such as pushdown automata [15,16,17,14,9,8], lossy channel systems [3,2], one-counter automata [7,5,6], or multicounter automata [18,11,10,21,12,4], which are finitely representable but the underlying game graph is infinite and sometimes even infinitelybranching (see, e.g., [11,10,21]). Since the properties of finite-state games do not carry over to infinite-state games in general (see, e.g., [20]), the above issues need to be revisited and clarified explicitly, which is the main goal of this paper.…”

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confidence: 99%

Determinacy in Stochastic Games with Unbounded Payoff Functions

Brázdil

Kučera

Novotný

2013

Mathematical and Engineering Methods in Computer Science

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We consider infinite-state turn-based stochastic games of two players, and , who aim at maximizing and minimizing the expected total reward accumulated along a run, respectively. Since the total accumulated reward is unbounded, the determinacy of such games cannot be deduced directly from Martin's determinacy result for Blackwell games. Nevertheless, we show that these games are determined both for unrestricted (i.e., history-dependent and randomized) strategies and deterministic strategies, and the equilibrium value is the same. Further, we show that these games are generally not determined for memoryless strategies. Then, we consider a subclass of -finitely-branching games and show that they are determined for all of the considered strategy types, where the equilibrium value is always the same. We also examine the existence and type of (ε-)optimal strategies for both players. IntroductionTurn-based stochastic games of two players are a standard model of discrete systems that exhibit both non-deterministic and randomized choice. One player (called or Max in this paper) corresponds to the controller who wishes to achieve/maximize some desirable property of the system, and the other player (called or Min) models the environment which aims at spoiling the property. Randomized choice is used to model events such as system failures, bit-flips, or coin-tossing in randomized algorithms.Technically, a turn-based stochastic game (SG) is defined as a directed graph where every vertex is either stochastic or belongs to one of the two players. Further, there is a fixed probability distribution over the outgoing transitions of every stochastic vertex. A play of the game is initiated by putting a token on some vertex. Then, the token is moved from vertex to vertex by the players or randomly. A strategy specifies how a player should play. In general, a strategy may depend on the sequence of vertices visited so far (we say that the strategy is history-dependent (H)), and it may specify a probability distribution over the outgoing transitions of the currently visited vertex rather than a single outgoing transtion (we say that the strategy is randomized (R)). Strategies that do not depend on the history of a play are called memoryless (M), and strategies that do not randomize (i.e., select a single outgoing transition) are called determinisctic (D). Thus, we obtain the MD, MR, HD, and HR strategy classes, where HR are unrestricted strategies and MD are the most restricted memoryless deterministic strategies.

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Stochastic Games with Lossy Channels

Cited by 17 publications

References 31 publications

Computable fixpoints in well-structured symbolic model checking

Computable fixpoints in well-structured symbolic model checking

Lossy Counter Machines Decidability Cheat Sheet

Determinacy in Stochastic Games with Unbounded Payoff Functions

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