Complexity of some problems in Petri nets

Jones, Neil D.; Landweber, Lawrence H.; Lien, Yao-Nan

doi:10.1016/0304-3975(77)90014-7

Cited by 205 publications

(97 citation statements)

References 12 publications

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“…Unfortunately, the results of [17] cannot be applied in our setting since the syntactic constraints require the absence of either duration or deadline both of which are necessary for translation of timed SDFGs to time Petri nets. [9] proves a general undecidability result for strict boundedness of time Petri net of [13]. However, in [2], two sufficient conditions are given for strict boundedness of time Petri nets.…”

Section: Related Workmentioning

confidence: 90%

Liveness and Boundedness of Synchronous Data Flow Graphs

Ghamarian

Geilen

Basten

et al. 2006

2006 Formal Methods in Computer Aided Design

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Section: Related Workmentioning

confidence: 90%

Liveness and Boundedness of Synchronous Data Flow Graphs

Ghamarian

Geilen

Basten

et al. 2006

2006 Formal Methods in Computer Aided Design

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“…For arbitrary TPNs, problem (1) is known undecidable from Jones et al (1977). It directly follows that (2), (4) and (5) are undecidable too.…”

Section: Decidable and Undecidable Propertiesmentioning

confidence: 97%

Reachability Problems and Abstract State Spaces for Time Petri Nets with Stopwatches

Berthomieu

Lime²,

Roux³

et al. 2007

Discrete Event Dyn Syst

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Several extensions of Time Petri nets (TPNs) have been proposed for modeling suspension and resumption of actions in timed systems. We first introduce a simple class of TPNs extended with stopwatches (SwTPNs), and present a semialgorithm for building exact representations of the behavior of SwTPNs, based on the known state class method for Time Petri nets. Then, we prove that state reachability in SwTPNs and all similar models is undecidable, even when bounded, which solves an open problem. Finally, we discuss overapproximation methods yielding finite abstractions of their behavior for a subclass of bounded SwTPNs, and propose a new one based on a quantization of the polyhedra representing temporal information. By adjusting a parameter, the exact behavior can be approximated as closely as desired. The methods have been implemented, experiments are reported.

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“…For instance, checking the absence of inconsistent states, which is the translation in the net of "no possible erroneous conclusions exist", implies to verify that some markings are not reachable, which can be very complex. In fact, the reachability problem, even for restricted classes of nets, has been shown to have a very high complexity [3]. Thus, the strategy of building the net and subsequent checking for reachable inconsistent states is infeasible.…”

Section: 6mentioning

confidence: 99%

Yeast: A case study for a practical use of formal methods

Inverardi¹,

Krishnamurthy

Yankelevich

1993

Lecture Notes in Computer Science

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This paper discusses a formal semantics for an existent event-action system, Yeast, developed at AT&T Bell Laboratories. Yeast is a good case study for the use of (trueconcurrent) semantic techniques since causal dependence among events, concurrency, nondeterminism and conflicting behaviour of specifications can all be modeled in Yeast. We discuss the use of the formalization in the verification of correctness of real Yeast applications with respect to various properties.

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Complexity of some problems in Petri nets

Cited by 205 publications

References 12 publications

Liveness and Boundedness of Synchronous Data Flow Graphs

Liveness and Boundedness of Synchronous Data Flow Graphs

Reachability Problems and Abstract State Spaces for Time Petri Nets with Stopwatches

Yeast: A case study for a practical use of formal methods

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