A well-structured framework for analysing petri net extensions

• Published in: Information and computation Vol. 195; no. 1; pp. 1 - 29
• Main Authors: Finkel, Alain, McKenzie, Pierre, Picaronny, Claudine
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.11.2004; Elsevier
• Subjects: 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
• DOI: 10.1016/j.ic.2004.01.005

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.