A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

A Kleene Theorem for Piecewise Constant Signals Automata

International audienceIn this paper, we consider timed automata for piecewise constant signals and prove that they recognize exactly the languages denoted by signal regular expressions with intersection and renaming. The main differences from the usual timed automata are: time elapses on transitions (passing through a state is instantaneous), signals may be split on a run on an automaton and constraints on transitions correspond to unions of open intervals but should be satisfied on closed intervals. This makes exact rendez-vous impossible. The paper stresses on the similarities and differences from the usual model

Equations on Timed Languages

. We continue investigation of languages, accepted by timed automata of Alur and Dill. In [ACM97] timed regular expressions equivalent to timed automata were introduced. Here we introduce quasilinear equations over timed languages with regular coefficients. We prove that the minimal solution of such an equation is regular and give an algorithm to calculate this solution. This result is used to obtain a new proof of Kleene theorem ([ACM97]) for timed automata. Equations over timed languages can be also considered as an alternative way of specifying these languages. 1 Introduction Timed automata ([AD94]) form the best investigated class of hybrid systems. It is known which problems about these automata are decidable and which are not, and there are tools for testing emptiness, evaluating reachable states etc. ([DOTY96]). However some theoretical aspects and parallels with ordinary finite automata are still not clear. This paper may be considered as a continuation of ([ACM97]) where time..