Equivalence of timed state machines and safe TPN

Haar, Stefan; Kaiser, Laurent; Simonot-Lion, Françoise; Toussaint, Joël

doi:10.1109/wodes.2002.1167678

Cited by 12 publications

(15 citation statements)

References 13 publications

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“…In another line of work [12], Haar, Kaiser, Simonot & Toussaint compare Timed State Machines and Time Petri Nets. They give a translation from one model to another that preserves timed languages.…”

Section: Introductionmentioning

confidence: 99%

Comparison of the Expressiveness of Timed Automata and Time Petri Nets

Bérard¹,

Cassez²,

Haddad³

et al. 2005

Lecture Notes in Computer Science

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Abstract. In this paper we consider the model of Time Petri Nets (TPN) "à la Merlin" where a time interval is associated with the firing of a transition, but we extend it with open intervals. We also consider Timed Automata (TA) as defined by Alur & Dill. We investigate some questions related to expressiveness for these models : we study the impact of slight variations of semantics for TPN and we compare the expressive power of TA and TPN, with respect to both time language acceptance and weak time bisimilarity. We prove that TA and bounded TPNs (enlarged with strict constraints) are equivalent w.r.t. timed language equivalence, providing an efficient construction of a TPN equivalent to a TA. We then exhibit a TA A such that no TPN (even unbounded) is weakly bisimilar to A. Because of this last result, it is natural to try and identify the (strict) subclass of TA that is equivalent to TPN w.r.t. weak timed bisimilarity. Thus we give some further results: 1) we characterize the subclass TA − of TA that is equivalent to the original model of TPN as defined by Merlin, i.e. restricted to closed intervals, 2) we show that the associated membership problem for TA − is P SP ACE-complete and 3) we prove that the reachability problem for TA − is also P SP ACE-complete.

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Section: Introductionmentioning

confidence: 99%

Comparison of the Expressiveness of Timed Automata and Time Petri Nets

Bérard¹,

Cassez²,

Haddad³

et al. 2005

Lecture Notes in Computer Science

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“…A translation from diagonal-free TA without invariants and strict constraints to 1-safe TPN preserving weak timed bisimulation was suggested by Haar et al in [49]. In the paper they, however, consider only weak (non-urgent) semantics for TPN.…”

Section: Relationships Among the Modelsmentioning

confidence: 99%

“…Haar et al provided in [49] a translation from 1-safe TPN to TA preserving weak timed bisimilarity. It improved the complexity of the previously known work based on enumerative methods [23,24] and their translation is polynomial but only in the size of the TPN reachability graph.…”

Section: Relationships Among the Modelsmentioning

confidence: 99%

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Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets

Srba

Lecture Notes in Computer Science

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Abstract. Time dependant models have been intensively studied for many reasons, among others because of their applications in software verification and due to the development of embedded platforms where reliability and safety depend to a large extent on the time features. Many of the time dependant models were suggested as real-time extensions of several well-known untimed models. The most studied formalisms include Networks of Timed Automata which extend the model of communicating finite-state machines with a finite number of real-valued clocks, and timed extensions of Petri nets where the added time constructs include e.g. time intervals that are assigned to the transitions (Time Petri Nets) or to the arcs (Timed-Arc Petri Nets). In this paper, we shall semiformally introduce these models, discuss their strengths and weaknesses, and provide an overview of the known results about the relationships among the models.

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“…In [18], the authors compare diagonalfree TAs without strict constraints and Safe-TPNs (i.e. TPNs where the number of tokens in a place is at most 1), and give a translation from TAs to Safe-TPNs which preserves timed languages.…”

Section: Time Petri Netsmentioning

confidence: 99%