28 research outputs found

    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

    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

    Games with Delays. A Frankenstein Approach

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    We investigate infinite games on finite graphs where the information flow is perturbed by nondeterministic signalling delays. It is known that such perturbations make synthesis problems virtually unsolvable, in the general case. On the classical model where signals are attached to states, tractable cases are rare and difficult to identify. Here, we propose a model where signals are detached from control states, and we identify a subclass on which equilibrium outcomes can be preserved, even if signals are delivered with a delay that is finitely bounded. To offset the perturbation, our solution procedure combines responses from a collection of virtual plays following an equilibrium strategy in the instant- signalling game to synthesise, in a Frankenstein manner, an equivalent equilibrium strategy for the delayed-signalling game

    Assume-Admissible Synthesis

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    In this paper, we introduce a novel rule for synthesis of reactive systems, applicable to systems made of n components which have each their own objectives. It is based on the notion of admissible strategies. We compare our novel rule with previous rules defined in the literature, and we show that contrary to the previous proposals, our rule defines sets of solutions which are rectangular. This property leads to solutions which are robust and resilient. We provide algorithms with optimal complexity and also an abstraction framework.Comment: 31 page

    Computer aided synthesis: a game theoretic approach

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    In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum games. The simple case of one-player games is strongly related to automata theory on infinite words. All along the article, we focus on general approaches to solve the studied problems, and we provide several illustrative examples as well as intuitions on the proofs.Comment: Invitation contribution for conference "Developments in Language Theory" (DLT 2017

    The Complexity of Rational Synthesis

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    We study the computational complexity of the cooperative and non-cooperative rational synthesis problems, as introduced by Kupferman, Vardi and co-authors. We provide tight results for most of the classical omega-regular objectives, and show how to solve those problems optimally

    On the existence of weak subgame perfect equilibria

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    Assume-Guarantee Synthesis for Concurrent Reactive Programs with Partial Information

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    Synthesis of program parts is very useful for concurrent systems. However, most synthesis approaches do not support common design tasks, like modifying a single process without having to re-synthesize or verify the whole system. Assume-guarantee synthesis (AGS) provides robustness against modifications of system parts, but thus far has been limited to the perfect information setting. This means that local variables cannot be hidden from other processes, which renders synthesis results cumbersome or even impossible to realize. We resolve this shortcoming by defining AGS in a partial information setting. We analyze the complexity and decidability in different settings, showing that the problem has a high worst-case complexity and is undecidable in many interesting cases. Based on these observations, we present a pragmatic algorithm based on bounded synthesis, and demonstrate its practical applicability on several examples

    Foundations of Software Science and Computation Structures

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    We study multi-player turn-based games played on (potentially infinite) directed graphs. An outcome is assigned to every play of the game. Each player has a preference relation on the set of outcomes which allows him to compare plays. We focus on the recently introduced notion of weak subgame perfect equilibrium (weak SPE). This is a variant of the classical notion of SPE, where players who deviate can only use strategies deviating from their initial strategy in a finite number of histories. Having an SPE in a game implies having a weak SPE but the contrary is generally false. We propose general conditions on the structure of the game graph and on the preference relations of the players that guarantee the existence of a weak SPE, that additionally is finite-memory. From this general result, we derive two large classes of games for which there always exists a weak SPE: (i) the games with a finite-range outcome function, and (ii) the games with a finite underlying graph and a prefix-independent outcome function. For the second class, we identify conditions on the preference relations that guarantee memoryless strategies for the weak SPE.Comment: 28 page

    Strategy Logic with Imperfect Information

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    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
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