Sets of Communicating Sequential Processes.A Topological Rough Set Framework

Abstract

Communicating Sequential Processes (CSP), is a theoretical framework for discussing concurrent phenomena [8]. Many authors studied the subject, some of them from topological point of view (metrics on processes, completeness and fix–point issues, etc.) In this paper, we begin an investigation into the nature of sets of communicating sequential processes. We employ rough set theory as an adequate tool to classify sets of processes. Sets of sequential processes arise naturally when one considers processes contained within specified bounds that provide their approximate description. Adopting the trace formalism, we may express those bounds in a natural way by means of containment of traces. We endow families of process traces and a fortiori, families of processes, with a rough set topology. We show that basic operators on processes preserve exact sets of processes and they are non–expansive (i.e., non–destructive in terminology of [8]) with respect to the metric D on rough sets [7], [6], restricted to exact sets of processes. We omit details due to imposed paper length. The reader will find those details in [5].