RATIONAL PROCESSES AND LINEAR SYSTEMS IN GSP

Article type: Research Article

Authors: Gabarró, J. | Serna, M.J.

Affiliations: Dept. de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain

Abstract: We introduce a new way of describing a subclass of CSP processes in the failures-divergence model. These processes will be called rational, by analogy with rational languages in formal language theory. Usually, rational languages are characterized as a solution of a linear system of equations. In this work we use a restricted set of CSP operators and recursion to define CSP-linear systems. We show that these systems are in many respects similar to linear systems in formal language theory. Our main result states that for linear systems the least fix point solution in a CPO can be obtained using Arden's lemma. Furthermore we give an alternative definition of the class of rational processes in terms of automata. Finally we analyze how the previous result can be extended to other semantic models.

DOI: 10.3233/FI-1995-2434

Journal: Fundamenta Informaticae, vol. 24, no. 3, pp. 283-302, 1995