Abstract. Metric Temporal Logic (MTL) is a prominent specification formalism for realtime systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with non-primitive recursive complexity. We also consider the model-checking problem for MTL: whether all words accepted by a given Alur-Dill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL— which includes invariance and time-bounded response properties—is also decidable. These results are quite surprising in that they contradict various claims to the contrary that have appeared in the literature. 1.

... Metric Interval Temporal Logic (MITL) as a fragment of the real-time logic Metric Temporal Logic (MTL) in which exact or punctual timing constraints are banned. Their main result showed that model checking and satisfiability for MITL are both EXPSPACE-Complete. Until recently, it was widely believed that admitting even the simplest punctual specifications in any linear-time temporal logic would automatically lead to undecidability. Although this was recently disproved, until now no punctual fragment of MTL was known to have even primitive recursive complexity (with certain decidable fragments having provably non-primitive recursive complexity). In this paper we identify a ‘co-flat ’ subset of MTL that is capable of expressing a large class of punctual specifications and for which model checking (although not satisfiability) has no complexity cost over MITL. Our logic is moreover qualitatively different from MITL in that it can express properties that are not timed-regular. Correspondingly, our decision procedures do not involve translating formulas into finite-state automata, but rather into certain kinds of reversal-bounded Turing machines. Using this translation we show that the model checking problem for our logic is EXPSPACE-Complete

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.

Abstract. We study two questions in the theory of timed automata concerning timed language inclusion of real-time programs modeled as timed pushdown automata in real-time specifications with just one clock. We show that if the specification B is modeled as a timed automaton with one clock, then the language inclusion problem L(A) ` L(B) for a timed pushdown automaton A is decidable. On the other hand, we show that the universality problem of timed visibly pushdown automata with only one clock is undecidable. Thus there is no algorithm to check language inclusion of real-time programs for specifications given by visibly pushdown specifications with just one clock.

Abstract. We consider the control problem for timed automata against specifications given as MTL formulas. The logic MTL is a linear-time timed temporal logic which extends LTL with timing constraints on modalities, and recently, its model-checking has been proved decidable in several cases. We investigate these decidable fragments of MTL (full MTL when interpreted over finite timed words, and Safety-MTL when interpreted over infinite timed words), and prove two kinds of results. (1) We first prove that, contrary to model-checking, the control problem is undecidable. Roughly, the computation of a lossy channel system could be encoded as a model-checking problem, and we prove here that a perfect channel system can be encoded as a control problem. (2) We then prove that if we fix the resources of the controller (by resources we mean clocks and constants that the controller can use), the control problem becomes decidable. This decidability result relies on properties of well (and better) quasi-orderings. 1

The stochastic temporal logic CSL can be used to describe formally properties of continuous-time Markov chains, and has been extended with expressions over states and actions to obtain the logic asCSL. However, properties referring to the probability of a finite sequence of timed events (such as “with probability at least 0.75, the system will be in state set A at time 5, then in state set B at time 7, then in state set C at time 20”) cannot be expressed in either CSL or asCSL. With the aim of increasing the expressive power of temporal logics for continuoustime Markov chains, we introduce the logic CSL TA and its model-checking algorithm. CSL TA extends CSL and asCSL by allowing the specification of timed properties through a deterministic one-clock timed automata. 1

In this work, we study decision problems related to timed automata with silent transitions (TAε) which strictly extend the expressiveness of timed automata (TA). First, we answer negatively a central question raised by the introduction of silent transitions: can we decide whether the language recognized by a TAε can be recognized by some TA? Then we establish in the framework of TAε some old open conjectures that O. Finkel has recently solved for TA. Its proofs follow a generic scheme which relies on the fact that only a finite number of configurations can be reached by a TA while reading a timed word. This property does not hold for TAε, the proofs in the framework of TAε thus require more elaborated arguments. We establish undecidability of complementability, minimization of the number of clocks, and closure under shuffle. We also show these results in the framework of infinite timed languages.

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Abstract. We solve some decision problems for timed automata which were raised by S. Tripakis in [Tri04] and by E. Asarin in [Asa04]. In particular, we show that one cannot decide whether a given timed automaton is determinizable or whether the complement of a timed regular language is timed regular. We show that the problem of the minimization of the number of clocks of a timed automaton is undecidable. It is also undecidable whether the shuffle of two timed regular languages is timed regular. We show that in the case of timed Büchi automata accepting infinite timed words some of these problems are Π 1 1-hard, hence highly undecidable (located beyond the arithmetical hierarchy). 1

ABSTRACT. Web services technology is emerging as the main pillar of service-oriented architectures (SOAs). This technology facilitates application integration by enabling programmatic access to applications through standard, XML-based languages and protocols. While much progress has been made toward providing basic interoperability among applications, there are still many needs and unexploited opportunities in this area. In particular, services in SOAs require richer description models than object or component interfaces since services are developed independently of clients. Hence, service descriptions need to include all the information needed by clients to understand if they can interact with a service and how. This paper discusses our new results on modeling and analyzing web services business protocols augmented with timing constraints. We discuss these notions informally through examples, and expose the benefits of connecting our new model with the theory of timed automata.