On the Step Branching Time Closure of Free-Choice Petri Nets

Abstract : Free-choice Petri nets constitute a non-trivial subclass of Petri nets, excelling in simplicity as well as in analyzability. Extensions of free-choice nets have been investigated and shown to be translatable back to interleaving-equivalent free-choice nets. In this paper, we investigate extensions of free-choice Petri nets up to step branching time equivalences. For extended free-choice nets, we achieve a generalization of the equivalence result by showing that an existing construction respects weak step bisimulation equivalence. The known translation for behavioral free-choice does not respect step branching time equivalences, which turns out to be a property inherent to all transformation functions from this net class into (extended) free-choice Petri nets. By analyzing the critical structures, we find two subsets of behavioral free-choice nets that are step branching time equivalent to free-choice nets. Finally, we provide a discussion concerning the actual closure of free-choice Petri nets up to step branching time equivalences.
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Erika Ábrahám; Catuscia Palamidessi. 34th Formal Techniques for Networked and Distributed Systems (FORTE), Jun 2014, Berlin, Germany. Springer, Lecture Notes in Computer Science, LNCS-8461, pp.232-248, 2014, Formal Techniques for Distributed Objects, Components, and Systems. 〈10.1007/978-3-662-43613-4_15〉
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Stephan Mennicke, Jens-Wolfhard Schicke-Uffmann, Ursula Goltz. On the Step Branching Time Closure of Free-Choice Petri Nets. Erika Ábrahám; Catuscia Palamidessi. 34th Formal Techniques for Networked and Distributed Systems (FORTE), Jun 2014, Berlin, Germany. Springer, Lecture Notes in Computer Science, LNCS-8461, pp.232-248, 2014, Formal Techniques for Distributed Objects, Components, and Systems. 〈10.1007/978-3-662-43613-4_15〉. 〈hal-01398018〉

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