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An algorithm for the general Petri net reachability problem
- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 2017 by ACM Inc.
- ISSN
- 1529-3785
- DOI
- 10.1145/3105908
- Publisher site
- See Article on Publisher Site
Abstract
The Logical View on Continuous Petri Nets MICHAEL BLONDIN, DIRO, Universit de Montr al, Canada, LSV, CNRS & ENS Cachan, Universit Paris-Saclay, France ALAIN FINKEL and CHRISTOPH HAASE, LSV, CNRS & ENS Cachan, Universit Paris-Saclay, France SERGE HADDAD, LSV, CNRS & ENS Cachan, Universit Paris-Saclay & INRIA, France Continuous Petri nets are a relaxation of classical discrete Petri nets in which transitions can be fired a fractional number of times, and consequently places may contain a fractional number of tokens. Such continuous Petri nets are an appealing object to study, since they over-approximate the set of reachable configurations of their discrete counterparts, and their reachability problem is known to be decidable in polynomial time. The starting point of this article is to show that the reachability relation for continuous Petri nets is definable by a sentence of linear size in the existential theory of the rationals with addition and order. Using this characterization, we obtain decidability and complexity results for a number of classical decision problems for continuous Petri nets. In particular, we settle the open problem about the precise complexity of reachability set inclusion. Finally, we show how continuous Petri nets can be incorporated inside the classical
Journal
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Aug 11, 2017