Thomas Brihaye

Improved undecidability results on weighted timed automata

A focused crawler is designed to traverse the Web to gather documents on a specific topic. It can be used to build domain-specific Web search portals and online personalized search tools. To estimate the relevance of a newly seen URL, it must use information gleaned from previously crawled page sequences.In this paper, we present a new approach for prediction of the links leading to relevant pages based on a Hidden Markov Model (HMM). The system consists of three stages: user data collection, user modelling via sequential pattern learning, and focused crawling. In particular, we first collect the Web pages visited during a user browsing session. These pages are clustered, and the link structure among pages from different clusters is then used to learn page sequences that are likely to lead to target pages. The learning is performed using HMM. During crawling, the priority of links to follow is based on a learned estimate of how likely the page is to lead to a target page. We compare the performance with Context-Graph crawling and Best-First crawling. Our experiments demonstrate that this approach performs better than Context-Graph crawling and Best-First crawling.

On O-Minimal Hybrid Systems

This paper is driven by a general motto: bisimulate a hybrid system by a finite symbolic dynamical system. In the case of o-minimal hybrid systems, the continuous and discrete components can be decoupled, and hence, the problem reduces in building a finite symbolic dynamical system for the continuous dynamics of each location. We show that this can be done for a quite general class of hybrid systems defined on o-minimal structures. In particular, we recover the main result of a paper by Lafferriere G., Pappas G.J. and Sastry S. on o-minimal hybrid systems.

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.

Probabilistic and topological semantics for timed automata

Like most models used in model-checking, timed automata are an idealized mathematical model used for representing systems with strong timing requirements. In such mathematical models, properties can be violated, due to unlikely (sequences of) events. We propose two new semantics for the satisfaction of LTL formulas, one based on probabilities, and the other one based on topology, to rule out these sequences. We prove that the two semantics are equivalent and lead to a PSPACE-Complete model-checking problem for LTL over finite executions.

On the expressiveness and decidability of o-minimal hybrid systems

This paper is driven by a general motto: bisimulate a hybrid system by a finite symbolic dynamical system. In the case of o-minimal hybrid systems, the continuous and discrete components can be decoupled, and hence, the problem reduces in building a finite symbolic dynamical system for the continuous dynamics of each location. We show that this can be done for a quite general class of hybrid systems defined on o-minimal structures. In particular, we recover the main result of a paper by G. Lafferriere, G.J. Pappas, and S. Sastry, on o-minimal hybrid systems. We also provide an analysis and extension of results on decidability and complexity of problems and constructions related to o-minimal hybrid systems.

Almost-Sure Model Checking of Infinite Paths in One-Clock Timed Automata

In this paper, we define two relaxed semantics (one based on probabilities and the other one based on the topological notion of largeness) for LTL over infinite runs of timed automata which rule out unlikely sequences of events. We prove that these two semantics match in the framework of single-clock timed automata (and only in that framework), and prove that the corresponding relaxed model-checking problems are PSPACE-Complete. Moreover, we prove that the probabilistic non-Zenoness can be decided for single-clocktimed automata in NLOGSPACE.

Quantitative Model-Checking of One-Clock Timed Automata under Probabilistic Semantics

In a probabilistic semantics for timed automata has been defined in order to rule out unlikely (sequences of) events. The qualitative model-checking problem for LTL properties has been investigated, where the aim is to check whether a given LTL property holds with probability 1 in a timed automaton, and solved for the class of single-clock timed automata. In this paper, we consider the quantitative model-checking problem for omega-regular properties: we aim at computing the exact probability that a given timed automaton satisfies an omega-regular property. We develop a framework in which we can compute a closed-form expression for this probability; we furthermore give an approximation algorithm,and finally prove that we can decide the threshold problem in that framework.

When Are Timed Automata Determinizable

In this paper, we propose an abstract procedure which, given a timed automaton, produces a language-equivalent deterministic infinite timed tree. We prove that under a certain boundedness condition, the infinite timed tree can be reduced into a classical deterministic timed automaton. The boundedness condition is satisfied by several subclasses of timed automata, some of them were known to be determinizable (event-clock timed automata, automata with integer resets), but some others were not. We prove for instance that strongly non-Zeno timed automata can be determinized. As a corollary of those constructions, we get for those classes the decidability of the universality and of the inclusion problems, and compute their complexities (the inclusion problem is for instance EXPSPACE-complete for strongly non-Zeno timed automata).

Control in o-minimal Hybrid Systems

In this paper, we consider the control of general hybrid systems. In this context we show that time-abstract bisimulation is not adequate for solving such a problem. That is why we consider other equivalence, namely the suffix equivalence based on the encoding of trajectories through words. We show that this suffix equivalence is in general a correct abstraction for control problems. We apply this result to o-minimal hybrid systems, and get decidability and computability results in this framework