## Paper: Axiomatizing net computations and processes (at LICS 1989)

**Pierpaolo Degano José Meseguer Ugo Montanari**

### Abstract

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 (Theor. Comput. Sci., vol.55, pp.87-136, 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

### BibTeX

@InProceedings{DeganoMeseguerMonta-Axiomatizingnetcomp, author = {Pierpaolo Degano and José Meseguer and Ugo Montanari}, title = {Axiomatizing net computations and processes}, booktitle = {Proceedings of the Fourth Annual IEEE Symposium on Logic in Computer Science (LICS 1989)}, year = {1989}, month = {June}, pages = {175--185}, location = {Pacific Grove, CA, USA}, publisher = {IEEE Computer Society Press} }