Véronique Bruyère

Acacia+, a tool for LTL synthesis

We present Acacia+, a tool for solving the LTL realizability and synthesis problems. We use recent approaches that reduce these problems to safety games, and can be solved efficiently by symbolic incremental algorithms based on antichains. The reduction to safety games offers very interesting properties in practice: the construction of compact solutions (when they exist) and a compositional approach for large conjunctions of LTL formulas.

Bertrand numeration systems and recognizability

Abstract There exist various well-known characterizations of sets of numbers recognizable by a finite automaton, when they are represented in some integer base p ⩾2. We show how to modify these characterizations, when integer bases p are replaced by linear numeration systems whose characteristic polynomial is the minimal polynomial of a Pisot number. We also prove some related interesting properties.

Model-Checking for Weighted Timed Automata

We study the model-checking problem for weighted timed automata and the weighted CTL logic by the bisimulation approach. Weighted timed automata are timed automata extended with costs on both edges and locations. When the costs act as stopwatches, we get stopwatch automata with the restriction that the stopwatches cannot be reset nor tested. The weighted CTL logic is an extension of TCTL that allow to reset and test the cost variables. Our main results are (i) the undecidability of the proposed model-checking problem for discrete and dense time, (ii) its PSpace-Completeness in the discrete case for a slight restriction of the logic, (iii) the precise frontier between finite and infinite bisimulations in the dense case for the subclass of stopwatch automata.

On optimal timed strategies

In this paper, we study timed games played on weighted timed automata. In this context, the reachability problem asks if, given a set T of locations and a cost C, Player 1 has a strategy to force the game into T with a cost less than C no matter how Player 2 behaves. Recently, this problem has been studied independently by Alur et al and by Bouyer et al. In those two works, a semi-algorithm is proposed to solve the reachability problem, which is proved to terminate under a condition imposing the non-zenoness of cost. In this paper, we show that in the general case the existence of a strategy for Player 1 to win the game with a bounded cost is undecidable. Our undecidability result holds for weighted timed game automata with five clocks. On the positive side, we show that if we restrict the number of clocks to one and we limit the form of the cost on locations, then the semi-algorithm proposed by Bouyer et al always terminates.

Automata on Linear Orderings

We consider words indexed by linear orderings. These extend finite, (bi-)infinite words and words on ordinals. We introduce automata and rational expressions for words on linear orderings. We prove that for countable scattered linear orderings they are equivalent. This result extends Kleenes theorem. The proofs are effective.

Durations, Parametric Model-Checking in Timed Automata with Presburger Arithmetic

We consider the problem of model-checking a parametric extension of the logic TCTL over timed automata and establish its decidability. Given a timed automaton, we show that the set of durations of runs starting from a region and ending in another region is definable in the arithmetic of Presburger (when the time domain is discrete) or in the theory of the reals (when the time domain is dense). With this logical definition, we show that the parametric model-checking problem for the logic TCTL can easily be solved. More generally, we are able to effectively characterize the values of the parameters that satisfy the parametric TCTL formula.

Real-Time Model-Checking: Parameters everywhere

In this paper, we study the model-checking and parameter synthesis problems of the logic TCTL over discrete-timed automata where parameters are allowed both in the model (timed automaton) and in the property (temporal formula). Our results are as follows. On the negative side, we show that the model-checking problem of TCTL extended with parameters is undecidable over discrete-timed automata with only one parametric clock. The undecidability result needs equality in the logic. On the positive side, we show that the model-checking and the parameter synthesis problems become decidable for a fragment of the logic where equality is not allowed. Our method is based on automata theoretic principles and an extension of our method to express durations of runs in timed automata using Presburger arithmetic.

Meet Your Expectations With Guarantees: Beyond Worst-Case Synthesis in Quantitative Games

We extend the quantitative synthesis framework by going beyond the worst-case. On the one hand, classical analysis of two-player games involves an adversary (modeling the environment of the system) which is purely antagonistic and asks for strict guarantees. On the other hand, stochastic models like Markov decision processes represent situations where the system is faced to a purely randomized environment: the aim is then to optimize the expected payoff, with no guarantee on individual outcomes. We introduce the beyond worst-case synthesis problem, which is to construct strategies that guarantee some quantitative requirement in the worst-case while providing an higher expected value against a particular stochastic model of the environment given as input. This problem is relevant to produce system controllers that provide nice expected performance in the everyday situation while ensuring a strict (but relaxed) performance threshold even in the event of very bad (while unlikely) circumstances. We study the beyond worst-case synthesis problem for two important quantitative settings: the mean-payoff and the shortest path. In both cases, we show how to decide the existence of finite-memory strategies satisfying the problem and how to synthesize one if one exists. We establish algorithms and we study complexity bounds and memory requirements.

Real-Time Model-Checking: Parameters Everywhere

In this paper, we study the model-checking and parameter synthesis problems of the logic TCTL over discrete-timed automata where parameters are allowed both in the model and in the property. We show that the model-checking problem of TCTL extended with parameters is undecidable over discrete-timed automata with only one parametric clock. The undecidability result needs equality in the logic. When equality is not allowed, we show that the model-checking and the parameter synthesis problems become decidable.

Equilibria in quantitative reachability games

In this paper, we study turn-based quantitative multiplayer non zero-sum games played on finite graphs with reachability objectives. In this framework each player aims at reaching his own goal as soon as possible. We prove existence of finite-memory Nash (resp. secure) equilibria in multiplayer (resp. two-player) games.