Whole-grain Petri Nets and Processes

Joachim Kock*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review


We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The formalism supports both a geometric semantics in the style of Goltz and Reisig (processes are etale maps from graphs) and an algebraic semantics in the style of Meseguer and Montanari, in terms of free coloured props, and allows the following unification: for P a Petri net, the Segal space of P-processes is shown to be the free coloured prop-in-groupoids on P. There is also an unfolding semantics à la Winskel, which bypasses the classical symmetry problems: with the new formalism, every Petri net admits a universal unfolding, which in turn has associated an event structure and a Scott domain. Since everything is encoded with explicit sets, Petri nets and their processes have elements. In particular, individual-token semantics is native. (Collective-token semantics emerges from rather drastic quotient constructions à la Best-Devillers, involving taking π0 of the groupoids of states.)

Original languageEnglish
Article number3559103
Pages (from-to)1-58
Number of pages58
JournalJournal of the ACM
Issue number1
Publication statusPublished - 20 Dec 2022


  • categorical semantics
  • graphs
  • hypergraphs
  • operational semantics
  • Petri nets
  • processes
  • unfolding


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