Solving Stochastic Büchi Games on Infinite Arenas with a Finite Attractor

Bertrand, Nathalie; Schnoebelen, Philippe

doi:10.4204/eptcs.117.8

Cited by 4 publications

(3 citation statements)

References 43 publications

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“…Finally, studies on quantitative game theory and related algorithms for determining the optimal strategies [26,118,122,25,14,37,99], conducted for various formalisms, like, e.g., automata, are particularly relevant, as such games can be used as models to define the interaction between a system and its environment on the base of quantitative objectives and behaviours inducing costs, rewards, and resource consumption. The relation with model checking is strict, as also demonstrated by the most recent advances in tools like, e.g., PRISM and MCMAS, implementing model checking algorithms for MDPs founded on game semantics.…”

Section: Analysis Techniques and Tools: Program Analysis Model Checkmentioning

confidence: 99%

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Aldini

2020

Electron. Proc. Theor. Comput. Sci.

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Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the behaviour of many critical systems and in estimating their properties. Hence, they need to be integrated both at the level of system modeling and within the verification methodologies and tools. Along the last two decades a variety of theoretical achievements and automated techniques have contributed to make quantitative modeling and verification mainstream in the research community. In the same period, they represented the central theme of the series of workshops entitled Quantitative Aspects of Programming Languages and Systems (QAPL) and born in 2001. The aim of this survey is to revisit such achievements and results from the standpoint of QAPL and its community.

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Section: Analysis Techniques and Tools: Program Analysis Model Checkmentioning

confidence: 99%

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Aldini

2020

Electron. Proc. Theor. Comput. Sci.

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“…Stochastic turn-based games were mostly studied for finite arenas, due to algorithmic concerns. There are notable exceptions of games with underlying tractable model, for which decidability result exist: recursive concurrent stochastic games [11,14], 1-counter stochastic games [9,10] or lossy channel systems [8,3]. For infinite arenas, general results mostly concern purely non-algorithmical, aspects, such as determinacy.…”

Section: Stochastic Gamesmentioning

confidence: 99%

Taming denumerable Markov decision processes with decisiveness

Bertrand¹,

Bouyer²,

Brihaye³

et al. 2020

Preprint

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Decisiveness has proven to be an elegant concept for denumerable Markov chains: it is general enough to encompass several natural classes of denumerable Markov chains, and is a sufficient condition for simple qualitative and approximate quantitative model checking algorithms to exist. In this paper, we explore how to extend the notion of decisiveness to Markov decision processes. Compared to Markov chains, the extra non-determinism can be resolved in an adversarial or cooperative way, yielding two natural notions of decisiveness. We then explore whether these notions yield model checking procedures concerning the infimum and supremum probabilities of reachability properties.

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“…Almost-sure Büchi objectives are decidable for this class, and pure memoryless strategies suffice for both players [AHdA + 08]. Generalized Büchi objectives are also decidable, and finite-memory strategies suffice for the player, while memoryless strategies suffice for the opponent [BS13].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Parity Games on Lossy Channel Systems

Abdulla

Clemente

Mayr

et al. 2013

Quantitative Evaluation of Systems

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ABSTRACT. We give an algorithm for solving stochastic parity games with almost-sure winning conditions on lossy channel systems, under the constraint that both players are restricted to finitememory strategies. First, we describe a general framework, where we consider the class of 2 1 2 -player games with almost-sure parity winning conditions on possibly infinite game graphs, assuming that the game contains a finite attractor. An attractor is a set of states (not necessarily absorbing) that is almost surely re-visited regardless of the players' decisions. We present a scheme that characterizes the set of winning states for each player. Then, we instantiate this scheme to obtain an algorithm for stochastic game lossy channel systems.

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Solving Stochastic Büchi Games on Infinite Arenas with a Finite Attractor

Cited by 4 publications

References 43 publications

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Taming denumerable Markov decision processes with decisiveness

Stochastic Parity Games on Lossy Channel Systems

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