A well-structured framework for analysing petri net extensions

Transition systems defined from recursive functions IN p → IN p are introduced and named WSNs, or well-structured nets. Such nets sit conveniently between Petri net extensions and general transition systems. In the first part of this paper, we study decidability properties of WSN classes obtained by...

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Veröffentlicht in:Information and computation Jg. 195; H. 1; S. 1 - 29
Hauptverfasser: Finkel, Alain, McKenzie, Pierre, Picaronny, Claudine
Format: Journal Article
Sprache:Englisch
Veröffentlicht: San Diego, CA Elsevier Inc 01.11.2004
Elsevier
Schlagworte:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Automata. Abstract machines. Turing machines
Computer science; control theory; systems
Exact sciences and technology
Theoretical computing
Transition system
Decidability
Computer theory
Recursive function
Well structured net
Computing
Algorithm
Petri net
ISSN:0890-5401, 1090-2651
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Zusammenfassung:Transition systems defined from recursive functions IN p → IN p are introduced and named WSNs, or well-structured nets. Such nets sit conveniently between Petri net extensions and general transition systems. In the first part of this paper, we study decidability properties of WSN classes obtained by imposing natural restrictions on their defining functions, with respect to termination, coverability, and four variants of the boundedness problem. We are able to precisely answer almost all the questions which arise, thus gaining much insight into old and new generalized Petri net decidability results. In the second part, we specialize our analysis to WSNs defined from affine functions, which elegantly encompass most Petri net extensions studied in the literature. Again, we study decidability properties of natural classes of affine WSN with respect to the above six computational problems. In particular, we develop an algorithm computing limits of iterated nonnegative affine functions, in order to decide the path-place variant of the boundedness problem for non-negative affine WSN.
ISSN:0890-5401
1090-2651
DOI:10.1016/j.ic.2004.01.005