Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model. We prove that model-checking SLii restricted to hierarchical instances is decidable. This result, because it allows for complex patterns of existential and universal quantification on strategies, greatly generalises previous ones, such as decidability of multi-player games with imperfect information and hierarchical observations, and decidability of distributed synthesis for hierarchical systems. To establish the decidability result, we introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL* with second-order quantification over atomic propositions) by parameterising its quantifiers with observations. The simple syntax of QCTL* ii allows us to provide a conceptually neat reduction of SLii to QCTL*ii that separates concerns, allowing one to forget about strategies and players and focus solely on second-order quantification. While the model-checking problem of QCTL*ii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. The decidability result for SLii follows since the reduction maps hierarchical instances of SLii to hierarchical formulas of QCTL*ii

Satisfiability Modulo Free Data Structures Combined with Bridging Functions

International audienceFree Data Structures are finite semantic trees modulo equational axioms that are useful to represent classical data structures such as lists, multisets and sets. We study the satisfiability problem when free data structures are combined with bridging functions. We discuss the possibility to get a combination methodàmethod`methodà la Nelson-Oppen for these particular non-disjoint unions of theories. In order to handle satisfiability problems with disequalities, we investigate a form of sufficient surjectivity for the bridging functions

Mixing Probabilistic and non-Probabilistic Objectives in Markov Decision Processes

In this paper, we consider algorithms to decide the existence of strategies in MDPs for Boolean combinations of objectives. These objectives are omega-regular properties that need to be enforced either surely, almost surely, existentially, or with non-zero probability. In this setting, relevant strategies are randomized infinite memory strategies: both infinite memory and randomization may be needed to play optimally. We provide algorithms to solve the general case of Boolean combinations and we also investigate relevant subcases. We further report on complexity bounds for these problems.Comment: Paper accepted to LICS 2020 - Full versio

Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, this problem is undecidable; but we introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model, and we prove that model-checking SLii restricted to hierarchical instances is decidable. To establish this result we go through QCTL, an intermediary, "low-level" logic much more adapted to automata techniques. QCTL is an extension of CTL with second-order quantification over atomic propositions. We extend it to the imperfect information setting by parameterising second-order quantifiers with observations. While the model-checking problem of QCTLii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. We apply our result to solve complex strategic problems in the imperfect-information setting. We first show that the existence of Nash equilibria for deterministic strategies is decidable in games with hierarchical information. We also introduce distributed rational synthesis, a generalisation of rational synthesis to the imperfect-information setting. Because it can easily be expressed in our logic, our main result provides solution to this problem in the case of hierarchical information.Comment: arXiv admin note: text overlap with arXiv:1805.1259

Interplays of Sure, Almost-Sure, and Threshold Parity Objectives on Markov Decision Processes

Two major approaches in synthesis consist in specifying either the worst case behaviour or specifying the stochastic behaviour of a system. This thesis aims at studying the interplays of sure and stochastic conditions by considering algorithms to decide the existence of strategies in Markov decision processes for combinations of objectives. These objectives are omega-regular properties expressed as parity conditions, that need to be enforced either surely, almost surely, or with some threshold probability. In this setting, relevant strategies are randomized infinite memory strategies: both infinite memory and randomization may be needed to play optimally. We provide algorithms and complexity bounds for three main problems. First, we study multiple sure objectives, and multiple almost-sure objectives. Second, we consider Boolean combinations of sure objectives and multiple almost-sure objectives. Third, we consider one sure objective, and stochastic objectives that have to hold with a given probability threshold.Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

A second-order well-balanced scheme for the shallow-water equations with topography

International audienceWe consider the well-balanced numerical scheme for the shallow-water equations with topography introduced in [8] and its second-order well-balanced extension, which requires two heuristic parameters. The goal of the present contribution is to derive a parameter-free second-order well-balanced scheme. To that end, we consider a convex combination between the well-balanced scheme and a second-order scheme. We then prove that a relevant choice of the parameter of this convex combination ensures that the resulting scheme is both second-order accurate and well-balanced. Afterwards, we perform several numerical experiments, in order to illustrate both the second-order accuracy and the well-balance property of this numerical scheme. Finally, we outline some perspectives in a short conclusion

Threshold constraints with guarantees for parity objectives in markov decision processes

The beyond worst-case synthesis problem was introduced recently by Bruyère et al. [10]: it aims at building system controllers that provide strict worst-case performance guarantees against an antagonistic environment while ensuring higher expected performance against a stochastic model of the environment. Our work extends the framework of [10] and follow-up papers, which focused on quantitative objectives, by addressing the case of ω-regular conditions encoded as parity objectives, a natural way to represent functional requirements of systems. We build strategies that satisfy a main parity objective on all plays, while ensuring a secondary one with sufficient probability. This setting raises new challenges in comparison to quantitative objectives, as one cannot easily mix different strategies without endangering the functional properties of the system. We establish that, for all variants of this problem, deciding the existence of a strategy lies in NP \ coNP, the same complexity class as classical parity games. Hence, our framework provides additional modeling power while staying in the same complexity class.SCOPUS: cp.pinfo:eu-repo/semantics/publishe

Les voix de L'Adolescence clémentine: Babel [En ligne], Hors-série Agrégation | 2019. Babel : Littératures plurielles, La Garde : Faculté des lettres, langues et sciences humaines - Université de Toulon

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