On Causal Semantics of Petri Nets

Rob J. van Glabbeek, Ursula Goltz, Jens-Wolfhard Schicke

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

We consider approaches for causal semantics of Petri nets, explicitly representing dependencies between transition occurrences. For one-safe nets or condition/event-systems, the notion of process as defined by Carl Adam Petri provides a notion of a run of a system where causal dependencies are reflected in terms of a partial order. A wellknown problem is how to generalise this notion for nets where places may carry several tokens. Goltz and Reisig have defined such a generalisation by distinguishing tokens according to their causal history. However, this so-called individual token interpretation is often considered too detailed. A number of approaches have tackled the problem of defining a more abstract notion of process, thereby obtaining a so-called collective token interpretation. Here we give a short overview on these attempts and then identify a subclass of Petri nets, called structural conflict nets, where the interplay between conflict and concurrency due to token multiplicity does not occur. For this subclass, we define abstract processes as equivalence classes of Goltz-Reisig processes. We justify this approach by showing that we obtain exactly one maximal abstract process if and only if the underlying net is conflict-free with respect to a canonical notion of conflict.
Original languageEnglish
Title of host publicationCONCUR 2011 -- Concurrency Theory: 22nd International Conference, CONCUR 2011, Aachen, Germany, September 6-9, 2011, Proceedings
EditorsJoost-Pieter Katoen, Barbara König
Place of PublicationBerlin, Heidelberg
PublisherSpringer Berlin Heidelberg
Pages43-59
Number of pages17
ISBN (Electronic)978-3-642-23217-6
ISBN (Print)978-3-642-23217-6
DOIs
Publication statusPublished - 9 Sept 2011
Event22nd International Conference on Concurrency Theory, 2011 - Aachen, Germany
Duration: 6 Sept 20119 Sept 2011
Conference number: 22

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Berlin, Heidelberg
Volume6901
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference22nd International Conference on Concurrency Theory, 2011
Abbreviated titleCONCUR 2011
Country/TerritoryGermany
CityAachen
Period6/09/119/09/11

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