Axiomatizing net computations and processes

Pierpaolo Degano, Jose Meseguer, Ugo Montanari

Research output: Chapter in Book/Report/Conference proceedingConference contribution


An algebraic axiomatization is proposed, where, given a net N, a term algebra P[N] with two operations of parallel and sequential composition is defined. The congruence classes generated by a few simple axioms are proved isomorphic to a slight refinement of classical processes. Actually, P[N] is a symmetric monoidal category, parallel composition is the monoidal operation on morphisms, and sequential composition is morphism composition. Besides P[N], the authors introduce a category S[N] containing the classical occurrence and step sequences. The term algebras of P[N] and S[N] are in general incomparable, and thus they introduce two more categories, K[N] and T[N], providing a most concrete and a most abstract extremum, respectively. The morphisms of T[N] are proved isomorphic to the processes recently defined in terms of the swap transformation by E. Best and R. Devillers (1987). Thus the diamond of the four categories gives a full account in algebraic terms of the relations between interleaving and partial ordering observations of place/transition net computations.

Original languageEnglish (US)
Title of host publicationProc Fourth Ann Symp Logic Comput Sci
Editors Anon
PublisherPubl by IEEE
Number of pages11
ISBN (Print)0818619546
StatePublished - 1989
Externally publishedYes
EventProceedings of the Fourth Annual Symposium on Logic in Computer Science - Pacific Grove, CA, USA
Duration: Jun 5 1989Jun 8 1989

Publication series

NameProc Fourth Ann Symp Logic Comput Sci


OtherProceedings of the Fourth Annual Symposium on Logic in Computer Science
CityPacific Grove, CA, USA

ASJC Scopus subject areas

  • Engineering(all)


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