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Axiomatizing the Algebra of Net Computations and Processes.

Degano, Pierpaolo; Meseguer, José; Montanari, Ugo

91: Technical Report TR--1. Università degli Studi di Pisa (Italy), Dipartimento di Informatica, 1991.

Also as: Technical Report SRI--CSL--90--12, pages 1-23 pp.. Menlo Park, CA, USA: SRI International, Computer Science Laboratory, November 1990.

Abstract: Descriptions of concurrent behaviour in terms of partial orderings have been recognized as superior when information about distribution in space, about causal dependency or about fairness must be provided. However, at least in the general case of Place/Transition nets, the proposed models lack a suitable, general notion of sequential composition. In this paper, a new algebraic axiomatization is proposed, where, given a net N, a term algebra PN 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.

Keywords: axiomatizing (the) algebra (of) net computation(s) (and) process(es); true concurrency; causal dependency; fairness; sequential composition; category theory.

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