# Raphaël Berthon's research while affiliated with Université Libre de Bruxelles and other places

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## Publications (15)

Active learning is a setting in which a student queries a teacher, through membership and equivalence queries, in order to learn a language. Performance on these algorithms is often measured in the number of queries required to learn a target, with an emphasis on costly equivalence queries. In graybox learning, the learning process is accelerated b...

Active learning is a setting in which a student queries a teacher, through membership and equivalence queries, in order to learn a language. Performance on these algorithms is often measured in the number of queries required to learn a target, with an emphasis on costly equivalence queries. In graybox learning, the learning process is accelerated b...

We introduce an extension of Strategy Logic for the imperfect-information setting, called SL ii 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 t...

We study alternating automata with qualitative semantics over infinite binary trees: Alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the automaton is accepting if almost all branches of the run are accepting. In this article, we prove a positive and...

In this paper, we consider algorithms to decide the existence of strategies in MDPs for Boolean combinations of objectives. These objectives are omega-regular properties that need to be enforced either surely, almost surely, existentially, or with non-zero probability. In this setting, relevant strategies are randomized infinite memory strategies:...

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 t...

We study alternating automata with qualitative semantics over infinite binary trees: alternation means that two opposing players construct a decoration of the input tree called a run, and the qualitative semantics says that a run of the automaton is accepting if almost all branches of the run are accepting. In this paper we prove a positive and a n...

We consider an extension of monadic second-order logic, interpreted over the infinite binary tree, by the qualitative path-measure quantifier. This quantifier says that the set of infinite paths in the tree satisfying a formula has Lebesgue-measure one. We prove that this logic is undecidable. To do this we prove that the emptiness problem of quali...

Alternating-time Temporal Logic (ATL*) is a central logic for multiagent systems. Its extension to the imperfect information setting (ATL*i ) is well known to have an undecidable model-checking problem when agents have perfect recall. Studies have thus mostly focused either on agents without memory, or on alternative semantics to retrieve decidabil...

We introduce an extension of Strategy logic for the imperfect-information setting, called SL ii , and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of " hierarchical instances " for which, intuitively, as one...

We introduce an extension of Strategy logic for the imperfect-information setting, called SL ii , and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of " hierarchical instances " for which, intuitively, as one...

The beyond worst-case synthesis problem was introduced recently by Bruy\`ere et al. [BFRR14]: it aims at building system controllers that provide strict worst-case performance guarantees against an antagonistic environment while ensuring higher expected performance against a stochastic model of the environment. Our work extends the framework of [BF...

Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend it to include imperfect information by parameterizing quantifiers with an observation that defines how well the...

## Citations

... This happens when e.g., the system has private and global variables, and the players model threads that can only view the global variables. To this end, games with partial information have been extensively studied in various forms [3,5,9,10]. However, in contrast to the full-information setting, the problem of deciding whether a partial-information multi-player game of infinite duration has a Nash equilibrium is not known to be decidable, and is known to be undecidable in the case of stochastic games [25]. ...

Reference: Concurrent Games with Multiple Topologies

... The logic MSO+∇ is expressive enough to encode the problem we study here, but this logic has been proved to be undecidable [3,7]. In [5,6], a fragment of MSO+∇, called thin MSO has been introduced. ...

... Computing Pun j (G PAR ) is polynomial in the size of M and exponential time in the size of priority functions set (de Alfaro and Henzinger 2000). Line 6 in the algorithm corresponds to checking the realisability problem for a qualitative parity logic formula containing conjunctions of almost-sure atoms over the MDP K −L resulting from G −L PAR when all players are as one, which can be solved in polynomial time (Berthon, Guha, and Raskin 2020). The formula expresses that the objective α ϕ (representing ϕ) is satisfied with probability 1, and each winning player i (that cannot be punished in M −L ) achieves its goal with probability 1. ...

... We have compared these approaches to ours in the beginning of Section 4. More generally, other restrictions on iCGS have been investigated recently, notably the hierarchical systems in [11,12], which are nonetheless orthogonal to the present setting. In particular, notice that no hierachy is assumed on the observations of agents in vCGS, nor anything similar appears in standard TF attacks. ...

... Finally, we want to target the distributed synthesis problem [20]. Several fragments of the problem have been proven to be decidable, e.g., when the information of agents is arranged hierarchically [13], the number of agents is limited [25], or the actions are made public [12]. We conjecture that the ability to disseminate information and reason about it might prove useful in this setting. ...

... Window parity objectives, especially bounded variants, are closely related to the notion of finitary ω-regular games, e.g., [18], and the semantics of prompt-ltl [29]. The window mechanism can be used to ensure a certain form of (local) guarantee over paths; different techniques have been considered in stochastic models [10,13,7]. Timed automata have numerous extensions, e.g., hybrid systems (e.g., [9] and references therein) and probabilistic timed automata (e.g., [32]); the window mechanism could prove useful in these richer settings. Finally, we recall that game models provide a framework for the synthesis of correct-by-construction controllers [34]. ...

... Goranko and van Drimmelen [17] gave a complete axiomatization of ATL. Decidability and model checking problems for ATLlike systems have also been studied [18,19,20]. Alternative approaches to expressing the power to achieve a goal in a temporal setting are the STIT logic [21,22,23,24,25] and Strategy Logic [26,27,19,28]. ...

Reference: Strategic Coalitions in Stochastic Games

... The latter extends CTL * with second-order quantification on atomic propositions, and it has been well studied [36,20,21,14,23]. QCTL * i , an imperfect-information extension of QCTL * , has recently been introduced, and its modelchecking problem was proven decidable for the class of hierarchical formulas [3]. In this paper we define a notion of hierarchical instances for the ATL * sc,i model-checking problem: an ATL * sc,i formula ϕ together with a concurrent game structure G is a hierarchical instance if the observations of agents appearing in strategy quantifiers get more refined as one goes down ϕ's syntactic tree. ...