Qualitative Determinacy and Decidability of Stochastic Games with Signals

Bertrand, Nathalie; Genest, Blaise; Gimbert, Hugo

doi:10.1109/lics.2009.31

Cited by 33 publications

(24 citation statements)

References 16 publications

(27 reference statements)

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“…These do not have perfect information on the history, but have to make their choices on the basis of what the corresponding agent has observed from the history (e.g., his own local states and actions). Such notions of randomized multi-agent systems have been studied in the context of distributed scheduling [Cheung et al 2006;Chatzikokolakis and Palamidessi 2010] or stochastic games with partial information [Gripon and Serre 2009;Bertrand et al 2009; and have concrete applications in security, for example, for information hiding [Andrés et al 2010]. Randomized multi-agent systems can be seen as multi-player variants of partially observable Markov decision processes (POMDP), that in turn generalize PBA.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic ω-automata

Baier

Größer

Bertrand

2012

J. ACM

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131

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Probabilistic ω-automata are variants of nondeterministic automata over infinite words where all choices are resolved by probabilistic distributions. Acceptance of a run for an infinite input word can be defined using traditional acceptance criteria for ω-automata, such as Büchi, Rabin or Streett conditions. The accepted language of a probabilistic ω-automata is then defined by imposing a constraint on the probability measure of the accepting runs. In this paper, we study a series of fundamental properties of probabilistic ω-automata with three different language-semantics: (1) the probable semantics that requires positive acceptance probability, (2) the almost-sure semantics that requires acceptance with probability 1, and (3) the threshold semantics that relies on an additional parameter λ ∈]0, 1[ that specifies a lower probability bound for the acceptance probability. We provide a comparison of probabilistic ω-automata under these three semantics and nondeterministic ω-automata concerning expressiveness and efficiency. Furthermore, we address closure properties under the Boolean operators union, intersection and complementation and algorithmic aspects, such as checking emptiness or language containment.

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Section: Introductionmentioning

confidence: 99%

Probabilistic ω-automata

Baier

Größer

Bertrand

2012

J. ACM

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131

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“…For example the qualitative analysis of simple stochastic games can be carried out in polynomial time [dA97] while for the quantitative analysis of these games only exponential time algorithms are known [Con92]. Even worse, for certain classes of stochastic games with partial observation the existence of almost-sure winning strategies is decidable whereas values are not computable [Paz71,CDHR07,BBG08,BGG09].…”

Section: Introductionmentioning

confidence: 99%

Solving Simple Stochastic Tail Games

Gimbert¹,

Horn²

2010

Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms

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Abstract. Stochastic games are a natural model for open reactive processes: one player represents the controller and his opponent represents a hostile environment. The evolution of the system depends on the decisions of the players, supplemented by random transitions. There are two main algorithmic problems on such games: computing the values (quantitative analysis) and deciding whether a player can win with probability 1 (qualitative analysis). In this paper we reduce the quantitative analysis to the qualitative analysis: we provide an algorithm for computing values which uses qualitative analysis as a sub-procedure. The correctness proof of this algorithm reveals several nice properties of perfect-information stochastic tail games, in particular the existence of optimal strategies. We apply these results to games whose winning conditions are boolean combinations of mean-payoff and Büchi conditions.

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“…Our model of game is equivalent to the model of stochastic games with signals [22,3] (in stochastic games with signals, the players receive signals which represent information about the game, which in our model is represented as observations). A probability distribution on a finite set A is a function κ : A → [0, 1] such that a∈A κ(a) = 1.…”

Section: Definitionsmentioning

confidence: 99%

Randomness for Free

Chatterjee

Doyen

Gimbert

et al. 2010

Mathematical Foundations of Computer Science 2010

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We consider two-player zero-sum games on finite-state 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) one-sided completeobservation (one player has complete observation); and (c) complete-observation (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) turn-based (players interact in turn). The two sources of randomness in these games are randomness in the transition function and randomness in the strategies. In general, randomized strategies are more powerful than deterministic strategies, and probabilistic transitions give 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 transitions can be simulated by deterministic transitions); and (b) strategies (pure strategies are as powerful as randomized strategies). As a consequence of our characterization we obtain new undecidability results for these games.

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Qualitative Determinacy and Decidability of Stochastic Games with Signals

Abstract: We consider the standard model of finite two-person zero-sum

Cited by 33 publications

References 16 publications

Probabilistic ω-automata

Probabilistic ω-automata

Solving Simple Stochastic Tail Games

Randomness for Free

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