Uniform Strategies

We consider turn-based game arenas for which we investigate uniformity properties of strategies. These properties involve bundles of plays, that arise from some semantical motive. Typically, we can represent constraints on allowed strategies, such as being observation-based. We propose a formal language to specify uniformity properties and demonstrate its relevance by rephrasing various known problems from the literature. Note that the ability to correlate different plays cannot be achieved by any branching-time logic if not equipped with an additional modality, so-called R in this contribution. We also study an automated procedure to synthesize strategies subject to a uniformity property, which strictly extends existing results based on, say standard temporal logics. We exhibit a generic solution for the synthesis problem provided the bundles of plays rely on any binary relation definable by a finite state transducer. This solution yields a non-elementary procedure.Comment: (2012

The Complexity of Synthesizing Uniform Strategies

We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is observation-based. We propose a formal language to specify uniformity properties, interpreted over two-player turn-based arenas equipped with a binary relation between plays. This way, we capture e.g. games with winning conditions expressible in epistemic temporal logic, whose underlying equivalence relation between plays reflects the observational capabilities of agents (for example, synchronous perfect recall). Our framework naturally generalizes many other situations from the literature. We establish that the problem of synthesizing strategies under uniformity constraints based on regular binary relations between plays is non-elementary complete.Comment: In Proceedings SR 2013, arXiv:1303.007

Emptiness Of Alternating Tree Automata Using Games With Imperfect Information

We consider the emptiness problem for alternating tree automata, with two acceptance semantics: classical (all branches are accepted) and qualitative (almost all branches are accepted). For the classical semantics, the usual technique to tackle this problem relies on a Simulation Theorem which constructs an equivalent non-deterministic automaton from the original alternating one, and then checks emptiness by a reduction to a two-player perfect information game. However, for the qualitative semantics, no simulation of alternation by means of non-determinism is known. We give an alternative technique to decide the emptiness problem of alternating tree automata, that does not rely on a Simulation Theorem. Indeed, we directly reduce the emptiness problem to solving an imperfect information two-player parity game. Our new approach can successfully be applied to both semantics, and yields decidability results with optimal complexity; for the qualitative semantics, the key ingredient in the proof is a positionality result for stochastic games played over infinite graphs

Dependency Matrices for Multiplayer Strategic Dependencies

In multi-player games, players take their decisions on the basis of their knowledge about what other players have done, or currently do, or even, in some cases, will do. An ability to reason in games with temporal dependencies between players\u27 decisions is a challenging topic, in particular because it involves imperfect information. In this work, we propose a theoretical framework based on dependency matrices that includes many instances of strategic dependencies in multi-player imperfect information games. For our framework to be well-defined, we get inspiration from quantified linear-time logic where each player has to label the timeline with truth values of the propositional variable she owns. We study the problem of the existence of a winning strategy for a coalition of players, show it is undecidable in general, and exhibit an interesting subclass of dependency matrices that makes the problem decidable: the class of perfect-information dependency matrices

Vers une synthèse d'arbres d'attaque pour une analyse de risques assistée par ordinateur

National audienceRisk Analysis is a discipline consisting in identifying and evaluating risks that threaten a given system in order to reduce or annihilate them by defining actions to engage (risk management). After (Bornette et al., 2005), we have developed a method aiming at building attack scenarios against a system that has to be protected. We describe this method in the present article. The main principle is to extract from a dedicated model of the system the scenarios (expressed as a succession of elementary actions) allowing to reach, from an initial state, a given goal (expressed as a set of damages against which we want to provide countermeasures). Thanks to the use of high-level actions, these scenarios are then gathered into an attack tree allowing after specific processing to highlight flaws to bring down.L'analyse de risques est une discipline consistant à identifier et à évaluer les risques qui menacent un système donné afin de les atténuer ou de les éliminer grâce à l'application de protocoles de sécurité (gestion de risques). Après (Bornette et al., 2005), nous avons développé une méthode ayant pour but de construire de façon automatique des scénarios d'attaque contre un système à protéger. Elle consiste principalement en l'extraction de ces scénarios, exprimés sous la forme de suites d'actions élémentaires permettant d'atteindre, à partir d'un état initial, un objectif donné (exprimé sous la forme d'un ensemble de dommages à causer au système), du graphe représentant le système. Grâce à l'utilisation d'une grammaire d'actions, nous en déduisons un arbre d'attaque mettant en évidence les failles du système étudié. Cette méthode doit aboutir à la conception d'un outil à destination des experts. Il ne leur reste alors qu'à déterminer des contremesures empêchant la réalisation effective de ses attaques

Automata Techniques for Epistemic Protocol Synthesis

International audienceIn this work we aim at applying automata techniques to problems studied in Dynamic Epistemic Logic, such as epistemic planning. To do so, we first remark that repeatedly executing ad infinitum a propositional event model from an initial epistemic model yields a relational structure that can be finitely represented with automata. This correspondence, together with recent results on uniform strategies, allows us to give an alternative decidability proof of the epistemic planning problem for propositional events, with as by-products accurate upper-bounds on its time complexity, and the possibility to synthesize a finite word automaton that describes the set of all solution plans. In fact, using automata techniques enables us to solve a much more general problem, that we introduce and call epistemic protocol synthesis

You can always compute maximally permissive controllers under partial observation when they exist

Abstract-The maximal permissivity property of controllers is an optimal criterion that is often taken for granted as the result of synthesis algorithms: the algorithms are designed for frameworks where the existence and the uniqueness of a maximal permissive controller is demonstrated apart, as it fulfills sufficient hypotheses ; these algorithms precisely compute this object. Still, maximally permissive solutions might exist in circumstances which do not fall into such identified frameworks, but there is no way to ensure that the algorithms deliver an optimal solution. In this paper, we propose a general synthesis procedure which always computes a maximal permissive controller when it exists

Emptiness Of Alternating Parity Tree Automata Using Games With Imperfect Information

We focus on the emptiness problem for alternating parity tree automata. The usual technique to tackle this problem first removes alternation, going to non-determinism, and then checks emptiness by reduction to a two-player perfect-information parity game. In this note, we give an alternative roadmap to this problem by providing a direct reduction to the emptiness problem to solving an imperfect-information two-player parity game.Nous considérons le problème du test du vide pour les automates d'arbres alternants à parité. La méthode usuelle pour résoudre ce problème, commence par supprimer l'alternance ce qui conduit à un automate non-déterministe dont le vide est ensuite testé par réduction à un jeux de parité à information parfaite. Dans cette note, nous proposons une approche alternative pour ce problème, en proposant une réduction directe du problème du vide à un jeu de parité à information imparfaite