Timed Petri Nets and BQOs

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.

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“…see [2]). Instead we recall some properties of bqo (see [2,3]), which will be used in the following.…”

Section: Well Quasi-orderings and Better Quasi-orderingsmentioning

confidence: 99%

Controller Synthesis for MTL Specifications

Bouyer

Bozzelli

Chevalier

2006

CONCUR 2006 – Concurrency Theory

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“…On the other hand, showing equivalence between WSTS classes is a problem deeply linked to the semantics of the models, and hence that remains to be solved on a case-by-case basis. TdPN [3] are Timed Petri nets and we have proved the related result in a companion report [5].…”

Section: Discussionmentioning

confidence: 59%

Ordinal Theory for Expressiveness of Well Structured Transition Systems

Bonnet

Finkel

Haddad

et al. 2011

Foundations of Software Science and Computational Structures

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Abstract. To the best of our knowledge, we characterize for the first time the importance of resources (counters, channels, alphabets) when measuring expressiveness of WSTS. We establish, for usual classes of wpos, the equivalence between the existence of order reflections (nonmonotonic order embeddings) and the simulations with respect to coverability languages. We show that the non-existence of order reflections can be proved by the computation of order types. This allows us to solve some open problems and to unify the existing proofs of the WSTS classification.

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“…On the other hand, coverability, boundedness and other problems remain decidable for TAPN [77,3,1], which are also known to offer 'weak' expressiveness, in the sense that TAPN cannot simulate Turing machines [25]. Coverability is decidable even for TAPN extended with read-arcs [30].…”

Section: Timed-arc Petri Netsmentioning

confidence: 99%

“…TAPN provide an easy to understand interplay between the token game and the associated time features. For modelling of certain applications, especially systems where a number of identical time processes share the same pattern of behaviour [3,4] but also others [70,79,80,71], TAPN provide a convenient modelling formalism. By simply adding more and more tokens to the net, more and more processes (each carrying its own clock) can be modelled without any change to the net itself.…”

Section: Timed-arc Petri Netsmentioning

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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Timed Petri Nets and BQOs

Cited by 112 publications

References 29 publications

Controller Synthesis for MTL Specifications

Controller Synthesis for MTL Specifications

Ordinal Theory for Expressiveness of Well Structured Transition Systems

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

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