Bastien Maubert

Opacity Issues in Games with Imperfect Information

We study in depth the class of games with opacity condition, which are two-player games with imperfect information in which one of the players only has imperfect information, and where the winning condition relies on the information he has along the play. Those games are relevant for security aspects of computing systems: a play is opaque whenever the player who has imperfect information never “knows” for sure that the current position is one of the distinguished “secret” positions. We study the problems of deciding the existence of a winning strategy for each player, and we call them the opacity-violate problemand the opacity-guarantee problem . Focusing on the player with perfect information is new in the field of games wi th imperfect-information because when considering classical winning conditions it amounts to solving the underlying perfect-information game. We establish the EXPTIME-completeness of both above-mentioned problems, showing that our winning condition brings a gap of complexity for the player with perfect information, and we exhibit the relevant opacity-verify problem, which noticeably generalizes approaches considered in the literature for opacity analysis in discrete-event syst ems. In the case of blindfold games, this problem relates to the two initial ones, yielding the determ inacy of blindfold games with opacity condition and the PSPACE-completeness of the three problems.

Tableau Method and NEXPTIME-Completeness of DEL-Sequents

Dynamic Epistemic Logic (DEL) deals with the representation of situations in a multi-agent and dynamic setting. It can express in a uniform way statements about:(i)what is true about an initial situation (ii)what is true about an event occurring in this situation (iii)what is true about the resulting situation after the event has occurred. After proving that what we can infer about (ii) given (i) and (iii) and what we can infer about (i) given (ii) and (iii) are both reducible to what we can infer about (iii) given (i) and (ii), we provide a tableau method deciding whether such an inference is valid. We implement it in LOTRECscheme and show that this decision problem is NEXPTIME-complete. This contributes to the proof theory and the study of the computational complexity of DEL which have rather been neglected so far.

Automata Techniques for Epistemic Protocol Synthesis.

In 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.

The Complexity of Synthesizing Uniform Strategies

We investigate uniformity properties of strategies. These properties involve sets of plays in ord er to express useful constraints on strategies that are not μ-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 equip ped 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 reflec ts 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 s ynthesizing strategies under uniformity constraints based on regular binary relations between plays is non-elementary complete.

Games with Opacity Condition

We describe the class of games with opacity condition, as an adequate model for security aspects of computing systems. We study their theoretical properties, relate them to reachability perfect information games and exploit this relation to discuss a search approach with heuristics, based on the directing-word problem in automata theory.

Reasoning about knowledge and messages in asynchronous multi-agent systems

We propose a variant of public announcement logic for asynchronous systems. To capture asynchrony, we introduce two different modal operators for sending and receiving messages. The natural approac ...

Relating Paths in Transition Systems: The Fall of the Modal Mu-Calculus

We revisit Janin and Walukiewicz’s classic result on the expressive completeness of the modal mu-calculus with respect to Monadic Second Order Logic (MSO), which is where the mu-calculus corresponds precisely to the fragment of MSO that is invariant under bisimulation. We show that adding binary relations over finite paths in the picture may alter the situation. We consider a general setting where finite paths of transition systems are linked by means of a fixed binary relation. This setting gives rise to natural extensions of MSO and the mu-calculus, that we call the MSO with paths relation and the jumping mu-calculus, the expressivities of which we aim at comparing. We first show that “bounded-memory” binary relations bring about no additional expressivity to either of the two logics, and thus preserve expressive completeness. In contrast, we show that for a natural, classic “infinite-memory” binary relation stemming from games with imperfect information, the existence of a winning strategy in such games, though expressible in the bisimulation-invariant fragment of MSO with paths relation, cannot be expressed in the jumping mu-calculus. Expressive completeness thus fails for this relation. These results crucially rely on our observation that the jumping mu-calculus has a tree automata counterpart: the jumping tree automata, hence the name of the jumping mu-calculus. We also prove that for observable winning conditions, the existence of winning strategies in games with imperfect information is expressible in the jumping mu-calculus. Finally, we derive from our main theorem that jumping automata cannot be projected, and ATL with imperfect information does not admit expansion laws.