On the Unification of Process Semantics: Equational Semantics

Authors:
David de Frutos Escrig;Carlos Gregorio Rodríguez;Miguel Palomino
Affiliations:
Departamento de Sistemas Informticos y Computacin, Universidad Complutense de Madrid;Departamento de Sistemas Informticos y Computacin, Universidad Complutense de Madrid;Departamento de Sistemas Informticos y Computacin, Universidad Complutense de Madrid
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2009

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Abstract

The complexity of parallel systems has produced a large collection of semantics for processes, a classification of which is provided by Van Glabbeek's linear time-branching time spectrum; however, no suitable unified definitions were available. We have discovered the way to unify them, both in an observational framework and by means of a quite small set of parameterized (in)equations that provide a sound and complete axiomatization of the preorders that define them. In more detail, we have proved that we only need a generic simulation axiom (NS), which defines the family of constrained simulation semantics, thus covering the class of branching time semantics, and a generic axiom (ND) for reducing the non-determinism of processes, by means of which we introduce the additional identifications induced by each of the linear time semantics.