In classical timed automata, as de ned by Alur and Dill [AD90, AD94] and widely since studied, the only operation allowed to modify the clocks is the reset operation. For instance, a clock can neither be set to a non-null constant value, nor be set to the value of another clock, nor, in a non-deterministic way, to some value lower or higher than a given constant. In this paper we study in details such updates which can be very useful for modelization purposes. We characterise in a thin way the frontier between decidable and undecidable. Our main contributions are the following: -- We exhibit many classes of updates for which emptiness is undecidable. A surprising result is that these classes depend on the clock constraints that are used diagonal-free or not whereas it is well known that these two kinds of constraints are equivalent for classical timed automata. -- We propose a generalization of the region automaton proposed by Alur and Dill to handle with larger classes of updates. ...

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Abstract. By definition Timed Automata have an infinite state-space, thus for verification purposes, an exact finite abstraction is required. We propose a locationbased finite zone abstraction, which computes an abstraction based on the relevant guards for a particular state of the model (as opposed to all guards). We show that the location-based zone abstraction is sound and complete with respect to location reachability; that it generalises active-clock reduction, in the sense that an inactive clock has no relevant guards at all; that it enlarges the class of timed automata, that can be verified. We generalise the new abstraction to the case of networks of timed automata, and experimentally demonstrate a potentially exponential speedup compared to the usual abstraction. 1

We propose in this paper a generalization of the famous Kleene/Büchi's theorem on formal languages, one of the cornerstones of theoretical computer science, to the timed model of clock languages. These languages extend the now classical timed languages introduced by Alur and Dill as a suitable model for real-time systems. As a corollary of our main result, we get a simple algebraic characterization of timed languages recognized by (updatable) timed automata.

www-verimag.imag.fr Abstract. Timed automata are known not to be complementable or determinizable. Natural questions are, then, could we check whether a given TA enjoys these properties? These problems are not algorithmically solvable, if we require not just a yes/no answer, but also a witness. Minimizing the “resources ” of a TA (number of clocks or size of constants) are also unsolvable problems. Proofs are provided as simple reductions from the universality problem. These proofs are not applicable to the corresponding decision problems, the decidability of which remains open. 1

Abstract. 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. 1

Timed Petri nets and timed automata are two standard models for the analysis of real-time systems. In this paper, we prove that they are incomparable for the timed language equivalence. Thus we propose an extension of timed Petri nets with read-arcs (RA-TdPN), whose coverability problem is decidable. We also show that this model unifies timed Petri nets and timed automata. Then, we establish numerous expressiveness results and prove that zeno behaviours discriminate between several sub-classes of RA-TdPNs. This has surprising consequences on timed automata, for instance on the power of non-deterministic clock resets.

Currently, formal verification of reactive, critical or embedded systems is a crucial problem, and automatic verification, more specifically model checking, has been widely developed during the last 20 years (see [CLA 99, SCH 01] for surveys). In this approach, we build a formal model M (e.g. an automaton, Petri net, etc.) describing

To study systems whose dynamics changes with time, an extension of timed P systems is introduced in which evolution rules may vary with time. The proposed model is a timed automaton with a discrete time domain and in which each state is a timed P system. A result on expressive power and on features of the formalism sufficient for full expressiveness is proved and, as an application example, the model of an ecological system is given.

Abstract. In this paper 4, we compare Timed Automata (TA) and Time Petri Nets (TPN) with respect to weak timed bisimilarity. It is already known that the class of bounded TPNs is strictly included in the class of TA. It is thus natural to try and identify the subclass T A wtb of TA equivalent to some TPN for the weak timed bisimulation relation. We give a characterization of this subclass and we show that the membership problem and the reachability problem for T A wtb are PSPACEcomplete. Furthermore we show that for a TA in T A wtb with integer constants, an equivalent TPN can be built with integer bounds but with a size exponential w.r.t. the original model. Surprisingly, using rational bounds yields a TPN whose size is linear.