Measuring Permissiveness in Parity Games: Mean-Payoff Parity Games Revisited

Bouyer, Patricia; Markey, Nicolas; Olschewski, Jörg; Ummels, Michael

doi:10.1007/978-3-642-24372-1_11

Cited by 25 publications

(43 citation statements)

References 23 publications

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“…We can now define the notion of multi-strategy (the use of this word is inspired by [9]). A multi-strategy indicates a set of actions that may be performed by an agent depending on the history of states already met.…”

Section: Semantic Frameworkmentioning

confidence: 99%

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A logic with revocable and refinable strategies

Chareton¹,

Brunel²,

Chemouil³

2015

Information and Computation

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In this article, we present Updatable Strategy Logic (USL), a multi-agent temporal logic which subsumes the main propositions in this area, such as ATL, ATL*, ATL sc and SL. These logics allow to express the capabilities of agents to ensure the satisfaction of temporal properties. USL mainly differs from SL, in two ways. Semantically, USL relies on multistrategies (that is, non-deterministic strategies), and the notion of strategy composition is extended to enable an agent to refine her strategy, that is to update it without revoking it. Syntactically, the logic features a binding operator enabling multi-strategy refinements as well as an "unbinding" operator that allows an agent to explicitly revoke a multi-strategy (whereas revocation is implicit with the binding operator in SL). We show that USL allows to express a notion of sustainable control for an agent, i.e., a capability to always decide the satisfaction of a property, that still holds even after the said capability has been employed. Furthermore, USL allows the definition of a notion of equality between multi-strategies that enables to consider quantification over deterministic strategies. This makes USL strictly more expressive than SL. Finally, we also show that the model-checking problem for USL is decidable but non-elementary (as for SL).

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Section: Semantic Frameworkmentioning

confidence: 99%

“…Intuitively, to win in the expert level, the magician needs complete information about the spectator's play; while in the beginner level, partial information only may be sufficient. Formula (9) expresses that the magician's multi-strategy strongly depends on the spectator's strategy in order to win the expert level game:…”

Section: Example 3 (Magic Trick)mentioning

confidence: 99%

A logic with revocable and refinable strategies

Chareton¹,

Brunel²,

Chemouil³

2015

Information and Computation

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“…The problem of 2-player mean-payoff parity games was first studied in [14]. The NP ∩ coNP complexity bound was established in [10], and an improved algorithm for the problem was given in [6]. The algorithmic analysis of 2 1 2 -player meanpayoff games has been studied in [1,4]: a reduction to 2 1 2 -player reachability games was presented in [1], and approximation schemes were considered in [4].…”

Section: Algorithmic Questions Inmentioning

confidence: 99%

“…For example, mean-payoff parity objectives are relevant in synthesis of optimal performance lock-synchronization for concurrent programs [8], where one player is the synchronizer, the opponent is the environment, and the randomization arises due to the randomized scheduler; the performance objective is specified as mean-payoff condition and the functional requirement (e.g., data-race freedom or liveness) as an ω-regular objective. Mean-payoff parity objectives have also been used in other applications such as to define permissivity for parity games [6]. Thus 2 1 2 -player mean-payoff parity games provide the theoretical foundation for analysis of stochastic reactive systems with functional as well as performance requirements.…”

Section: Introductionmentioning

confidence: 99%

Perfect-Information Stochastic Mean-Payoff Parity Games

Chatterjee

Doyen

Gimbert

et al. 2014

Lecture Notes in Computer Science

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The theory of graph games is the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic processes, we use 2 1 2 -player games where some transitions of the game graph are controlled by two adversarial players, the System and the Environment, and the other transitions are determined probabilistically. We consider 2 1 2 -player games where the objective of the System is the conjunction of a qualitative objective (specified as a parity condition) and a quantitative objective (specified as a mean-payoff condition). We establish that the problem of deciding whether the System can ensure that the probability to satisfy the mean-payoff parity objective is at least a given threshold is in NP ∩ coNP, matching the best known bound in the special case of 2-player games (where all transitions are deterministic). We present an algorithm running in time O(d · n 2d · MeanGame) to compute the set of almost-sure winning states from which the objective can be ensured with probability 1, where n is the number of states of the game, d the number of priorities of the parity objective, and MeanGame is the complexity to compute the set of almost-sure winning states in 2 1 2 -player mean-payoff games. Our results are useful in the synthesis of stochastic reactive systems with both functional requirement (given as a qualitative objective) and performance requirement (given as a quantitative objective).

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“…Models with both positive and negative weights have also been studied, but mostly qualitative behaviours alone have been analyzed (this is the case in counter automatasee [HKOW09,GHOW10,Haa12] for recent references), or quantitative constraints have been analyzed (in weighted Kripke structures or games [CDHR10,CRR12]). Mixing qualitative logical properties and quantitative constraints has only poorly been addressed so far, and many works only consider specifications given as a conjunction of a qualitative logical property and a quantitative constraint: this is for instance the case of optimal reachability, mean-payoff parity games [BMOU11], energy parity games [CD12], mean-payoff LTL synthesis [BBFR13].…”

Section: Introductionmentioning

confidence: 99%

Quantitative Verification of Weighted Kripke Structures

Bouyer

Gardy

Markey

2014

Automated Technology for Verification and Analysis

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Abstract. Extending formal verification techniques to handle quantitative aspects, both for the models and for the properties to be checked, has become a central research topic over the last twenty years. Following several recent works, we study model checking for (one-dimensional) weighted Kripke structures with positive and negative weights, and temporal logics constraining the total and/or average weight. We prove decidability when only accumulated weight is constrained, while allowing average-weight constraints alone already is undecidable.

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Measuring Permissiveness in Parity Games: Mean-Payoff Parity Games Revisited

Cited by 25 publications

References 23 publications

A logic with revocable and refinable strategies

A logic with revocable and refinable strategies

Perfect-Information Stochastic Mean-Payoff Parity Games

Quantitative Verification of Weighted Kripke Structures

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