Functorial models for Petri nets

Roberto Bruni, José Meseguer, Ugo Montanari, Vladimiro Sassone

Research output: Contribution to journalArticlepeer-review

Abstract

We show that although the algebraic semantics of place/transition Petri nets under the collective token philosophy can be fully explained in terms of strictly symmetric monoidal categories, the analogous, construction under the individual token philosophy is not completely satisfactory, because it lacks universality and also functoriality. We introduce the notion of pre nets to overcome this, obtaining a fully satisfactory categorical treatment, where the operational semantics of nets yields an adjunction. This allows us to present a uniform logical description of net behaviors under both the collective and the individual token philosophies in terms of theories and theory morphisms in partial membership equational logic. Moreover, since the universal property of adjunctions guarantees that colimit constructions on nets are preserved in our algebraic models, the resulting semantic framework has good compositional properties.

Original languageEnglish (US)
Pages (from-to)207-236
Number of pages30
JournalInformation and Computation
Volume170
Issue number2
DOIs
StatePublished - Nov 1 2001
Externally publishedYes

Keywords

  • Collective/individual token philosophy
  • Concurrent transition systems
  • Configuration structures
  • Monoidal categories
  • PT Petri nets
  • Partial membership equational logic
  • Pre-nets

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Computer Science Applications
  • Computational Theory and Mathematics

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