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Uniform strategies

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 Sophie Pinchinat
Le mardi 29 novembre 2011 à 11:00
Salle de Conférence (Pavillon des Jardins)
Sophie Pinchinat (IRISA, Université de Rennes 1)

Imperfect information games are becoming very popular for their ability to model interaction under uncertainty. Examples of this kind of situations are many, e.g. distributed features of computing systems, attacker's dialog with a security system, etc. Also, such games naturally arise in logic, e.g. as satisfiability games for mu-calculus formulas. Recently, some kind of imperfect information games have been used to provide the semantics of logics, as for Dependence Logic.

We propose the notion of "uniform strategy" which unifies the aforementioned approaches, and even provides new model-checking games for complex logics, e.g. combining time and knowledge. Our definition relies on pairs of parameters : an equivalence relation between plays, and a uniformity condition over sets of equivalent plays. Basically, a strategy is uniform if the equivalence class of any play induced by the strategy satisfies the uniformity condition. For example, the equivalence can arise from a player ability to observe and recall what happened during the play (The perfect recall-imperfect recall spectrum lies in this parameter). Additionally, the uniformity condition can express many aspects. It can capture the nature of the strategy, e.g. that it is observation-based, as needed in the very standard imperfect information games setting. It can characterize non-regular properties of strategies, e.g. that strategies maintain the opponent's uncertainty about some secret, as considered in games with opacity condition.

In this talk, we will explain and motivate our notion of uniform strategy, and relate it to various examples from the literature: namely, imperfect information games, games with opacity condition, emptiness of alternating automata, first-order dependence logic model-checking games, epistemic temporal logic model-checking games. If time left, we will address decidability and complexity issues by scanning computational hypothesis one may require on the pair of parameters.

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