TY - GEN

T1 - Axiomatizing net computations and processes

AU - Degano, Pierpaolo

AU - Meseguer, Jose

AU - Montanari, Ugo

PY - 1989/12/1

Y1 - 1989/12/1

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:0024913454

SN - 0818619546

T3 - Proc Fourth Ann Symp Logic Comput Sci

SP - 175

EP - 185

BT - Proc Fourth Ann Symp Logic Comput Sci

A2 - Anon, null

PB - Publ by IEEE

T2 - Proceedings of the Fourth Annual Symposium on Logic in Computer Science

Y2 - 5 June 1989 through 8 June 1989

ER -