A well-structured framework for analysing petri net extensions

  • Authors:

  • Alain Finkel;Pierre McKenzie;Claudine Picaronny

  • Affiliations:

  • Laboratoire Spécification et Vérification (CNRS URA 8643), ícole Normale Supérieure de Cachan, 61, Avenue du Président Wilson, 94235 Cachan Cedex, France ENS Cachan;Informatique et recherche opérationnelle, Université de Montréal, C.P. 6128, succ. Centre-Ville, Montréal, Que., Canada H3C 3J7;Laboratoire Spécification et Vérification (CNRS URA 8643), ícole Normale Supérieure de Cachan, 61, Avenue du Président Wilson, 94235 Cachan Cedex, France ENS Cachan

  • Venue:
  • Information and Computation
  • Year:
  • 2004

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Abstract

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.