# Thomas Brihaye - Université de Mons

## Contact Details

NameThomas Brihaye |
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AffiliationUniversité de Mons |
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CityMons |
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CountryBelgium |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesComputer Science - Logic in Computer Science (12) Computer Science - Computer Science and Game Theory (10) Mathematics - Logic (1) Computer Science - Software Engineering (1) |

## Publications Authored By Thomas Brihaye

A decade ago, Abdulla et al introduced the elegant concept of decisiveness for denumerable Markov chains [1]. Roughly decisiveness allows one to lift most good properties from finite Markov chains to denumerable ones, and therefore to adapt existing verification algorithms to infinite-state models. Denumerable Markov chains however do not encompass stochastic real-time systems, and general stochastic transition systems (STSs) are needed. Read More

**Authors:**Thomas Brihaye

^{1}, Amit Kumar Dhar

^{2}, Gilles Geeraerts

^{3}, Axel Haddad

^{4}, Benjamin Monmege

^{5}

**Affiliations:**

^{1}UMONS, Mons, Belgium,

^{2}IIITA, Allahabad, India,

^{3}ULB, Brussels, Belgium,

^{4}UMONS, Mons, Belgium,

^{5}LIF, Aix-Marseille Univ, CNRS, Marseille, France

Algorithms and models based on game theory have nowadays become prominent techniques for the design of digital controllers for critical systems. Indeed, such techniques enable automatic synthesis: given a model of the environment and a property that the controller must enforce, those techniques automatically produce a correct controller, when it exists. In the present paper, we consider a class of concurrent, weighted, multi-player games that are well-suited to model and study the interactions of several agents who are competing for some measurable resources like energy. Read More

This volume contains the joint proceedings of the Workshop on Games for the Synthesis of Complex Systems (CASSTING'16) and of the 3rd International Workshop on Synthesis of Complex Parameters (SynCoP'16). The workshops were held in Eindhoven, The Netherlands, as satellite events of the 19th European Joint Conferences on Theory and Practice of Software (ETAPS'16). Both workshops are closely related in their topics as well as target audience and they shared a joint invited talk given by Giorgio Delzanno. Read More

We study the reactive synthesis problem (RS) for specifications given in Metric Interval Temporal Logic (MITL). RS is known to be undecidable in a very general setting, but on infinite words only; and only the very restrictive BRRS subcase is known to be decidable (see D'Souza et al. and Bouyer et al. Read More

Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modeling the costs of spending time in a state and executing an action, respectively). The goals of the players are to minimise and maximise the cost to reach a target location, respectively. We consider priced timed games with one clock and arbitrary (positive and negative) weights and show that, for an important subclass of theirs (the so-called simple priced timed games), one can compute, in exponential time, the optimal values that the players can achieve, with their associated optimal strategies. Read More

We study a generalisation of sabotage games, a model of dynamic network games introduced by van Benthem. The original definition of the game is inherently finite and therefore does not allow one to model infinite processes. We propose an extension of the sabotage games in which the first player (Runner) traverses an arena with dynamic weights determined by the second player (Saboteur). Read More

We study $n$-player turn-based games played on a finite directed graph. For each play, the players have to pay a cost that they want to minimize. Instead of the well-known notion of Nash equilibrium (NE), we focus on the notion of subgame perfect equilibrium (SPE), a refinement of NE well-suited in the framework of games played on graphs. Read More

**Authors:**Nathalie Bertrand

^{1}, Patricia Bouyer

^{2}, Thomas Brihaye

^{3}, Quentin Menet

^{4}, Christel Baier

^{5}, Marcus Groesser

^{6}, Marcin Jurdzinski

^{7}

**Affiliations:**

^{1}INRIA Rennes - Bretagne Atlantique,

^{2}LSV & ENS Cachan,

^{3}Université de Mons,

^{4}Université de Mons,

^{5}Technische Universität Dresden,

^{6}Technische Universität Dresden,

^{7}University of Warwick

A stochastic timed automaton is a purely stochastic process defined on a timed automaton, in which both delays and discrete choices are made randomly. We study the almost-sure model-checking problem for this model, that is, given a stochastic timed automaton A and a property $\Phi$, we want to decide whether A satisfies $\Phi$ with probability 1. In this paper, we identify several classes of automata and of properties for which this can be decided. Read More

Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the sum of the weights. Our aim is to describe the first pseudo-polynomial time algorithm for total-payoff games in the presence of arbitrary weights. Read More

One clock alternating timed automata (OCATA) have been introduced as natural extension of (one clock) timed automata to express the semantics of MTL. In this paper, we consider the application of OCATA to the problems of model-checking and satisfiability for MITL (a syntactic fragment of MTL), interpreted over infinite words. Our approach is based on the interval semantics (recently introduced in [BEG13] in the case of finite words) extended to infinite words. Read More

Priced timed games (PTGs) are two-player zero-sum games played on the infinite graph of configurations of priced timed automata where two players take turns to choose transitions in order to optimize cost to reach target states. Bouyer et al. and Alur, Bernadsky, and Madhusudan independently proposed algorithms to solve PTGs with nonnegative prices under certain divergence restriction over prices. Read More

The languages of infinite timed words accepted by timed automata are traditionally defined using Buchi-like conditions. These acceptance conditions focus on the set of locations visited infinitely often along a run, but completely ignore quantitative timing aspects. In this paper we propose a natural quantitative semantics for timed automata based on the so-called frequency, which measures the proportion of time spent in the accepting locations. Read More

**Affiliations:**

^{1}University of Mons,

^{2}University of Mons

In 2006, Varacca and V\"olzer proved that on finite graphs, omega-regular large sets coincide with omega-regular sets of probability 1, by using the existence of positional strategies in the related Banach-Mazur games. Motivated by this result, we try to understand relations between sets of probability 1 and various notions of simple strategies (including those introduced in a recent paper of Gr\"adel and Lessenich). Then, we introduce a generalisation of the classical Banach-Mazur game and in particular, a probabilistic version whose goal is to characterise sets of probability 1 (as classical Banach-Mazur games characterise large sets). Read More

One clock alternating timed automata OCATA have been recently introduced as natural extension of (one clock) timed automata to express the semantics of MTL (Ouaknine, Worrell 2005). We consider the application of OCATA to problem of model-checking MITL formulas (a syntactic fragment of MTL) against timed automata. We introduce a new semantics for OCATA where, intuitively, clock valuations are intervals instead of single real values. Read More

In this paper, we study thetime-bounded reachability problem for rectangular hybrid automata with non-negative rates (RHA+). This problem was recently shown to be decidable [Brihaye et al, ICALP11] (even though the unbounded reachability problem for even very simple classes of hybrid automata is well-known to be undecidable). However, [Brihaye et al, ICALP11] does not provide a precise characterisation of the complexity of the time-bounded reachability problem. Read More

Multiplayer games with selfish agents naturally occur in the design of distributed and embedded systems. As the goals of selfish agents are usually neither equivalent nor antagonistic to each other, such games are non zero-sum games. We study such games and show that a large class of these games, including games where the individual objectives are mean- or discounted-payoff, or quantitative reachability, and show that they do not only have a solution, but a simple solution. Read More

We study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In such games, each player aims at reaching his own goal set of states as soon as possible. A previous work on this model showed that Nash equilibria (resp. Read More

In this paper, we study turn-based quantitative multiplayer non zero-sum games played on finite graphs with both reachability and safety objectives. In this framework a player with a reachability objective aims at reaching his own goal as soon as possible, whereas a player with a safety objective aims at avoiding his bad set or, if impossible, delaying its visit as long as possible. We prove the existence of Nash equilibria with finite memory in quantitative multiplayer reachability/safety games. Read More

This paper investigates the time-bounded version of the reachability problem for hybrid automata. This problem asks whether a given hybrid automaton can reach a given target location within T time units, where T is a constant rational value. We show that, in contrast to the classical (unbounded) reachability problem, the timed-bounded version is decidable for rectangular hybrid automata provided only non-negative rates are allowed. Read More

In this paper, we consider reachability games over general hybrid systems, and distinguish between two possible observation frameworks for those games: either the precise dynamics of the system is seen by the players (this is the perfect observation framework), or only the starting point and the delays are known by the players (this is the partial observation framework). In the first more classical framework, we show that time-abstract bisimulation is not adequate for solving this problem, although it is sufficient in the case of timed automata . That is why we consider an other equivalence, namely the suffix equivalence based on the encoding of trajectories through words. Read More