2,856 research outputs found

    The Complexity of Admissibility in Omega-Regular Games

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    Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games played on graphs with omega-regular objectives. In this paper, we study the algorithmic properties of this concept for such games. We settle the exact complexity of natural decision problems on the set of strategies that survive iterated elimination of dominated strategies. As a byproduct of our construction, we obtain automata which recognize all the possible outcomes of such strategies

    Non-Zero Sum Games for Reactive Synthesis

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    In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.Comment: LATA'16 invited pape

    Minimizing Running Costs in Consumption Systems

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    A standard approach to optimizing long-run running costs of discrete systems is based on minimizing the mean-payoff, i.e., the long-run average amount of resources ("energy") consumed per transition. However, this approach inherently assumes that the energy source has an unbounded capacity, which is not always realistic. For example, an autonomous robotic device has a battery of finite capacity that has to be recharged periodically, and the total amount of energy consumed between two successive charging cycles is bounded by the capacity. Hence, a controller minimizing the mean-payoff must obey this restriction. In this paper we study the controller synthesis problem for consumption systems with a finite battery capacity, where the task of the controller is to minimize the mean-payoff while preserving the functionality of the system encoded by a given linear-time property. We show that an optimal controller always exists, and it may either need only finite memory or require infinite memory (it is decidable in polynomial time which of the two cases holds). Further, we show how to compute an effective description of an optimal controller in polynomial time. Finally, we consider the limit values achievable by larger and larger battery capacity, show that these values are computable in polynomial time, and we also analyze the corresponding rate of convergence. To the best of our knowledge, these are the first results about optimizing the long-run running costs in systems with bounded energy stores.Comment: 32 pages, corrections of typos and minor omission

    Infinite Horizon Noncooperative Differential Games with Non-Smooth Costs

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    In the present paper, we consider a class of two players infinite horizon differential games, with piecewise smooth costs exponentially discounted in time. Through the analysis of the value functions, we study in which cases it is possible to establish the existence Nash equilibrium solutions in feedback form. We also provide examples of piecewise linear costs whose corresponding games have either infinitely many Nash equilibria or no solutions at all.Comment: 17 pages, 5 figure

    How to Handle Assumptions in Synthesis

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    The increased interest in reactive synthesis over the last decade has led to many improved solutions but also to many new questions. In this paper, we discuss the question of how to deal with assumptions on environment behavior. We present four goals that we think should be met and review several different possibilities that have been proposed. We argue that each of them falls short in at least one aspect.Comment: In Proceedings SYNT 2014, arXiv:1407.493

    Infinite Horizon Noncooperative Differential Games

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    For a non-cooperative differential game, the value functions of the various players satisfy a system of Hamilton-Jacobi equations. In the present paper, we consider a class of infinite-horizon games with nonlinear costs exponentially discounted in time. By the analysis of the value functions, we establish the existence of Nash equilibrium solutions in feedback form and provide results and counterexamples on their uniqueness and stability.Comment: 25 pages, 7 figure

    The descriptive theory of represented spaces

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    This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented spaces. Most material is from work-in-progress, and thus there may be a stronger focus on projects involving the author than an objective survey would merit.Comment: survey of work-in-progres

    Value without absolute convergence

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    We address how the value of risky options should be assessed in the case where the sum of the probability-weighted payoffs is not absolutely convergent and thus dependent on the order in which the terms are summed (e.g., as in the Pasadena Paradox). We develop and partially defend a proposal according to which options should be evaluated on the basis of agreement among admissible (e.g., convex and quasi-symmetric) covering sequences of the constituents of value (i.e., probabilities and payoffs).
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