Some Remarks on Sets of Communicating Sequential Processes in Topological Rough Set Framework

  • Authors:

  • Lech Polkowski;Maria Semeniuk-Polkowska

  • Affiliations:

  • Polish-Japanese Institute of Information Technology, Koszykowa 86, 02008 Warszawa, Poland;Chair of Formal Linguistics, Warsaw University, Browarna 8/10, 00901 Warszawa, Poland

  • Venue:
  • Fundamenta Informaticae - Concurrency Specification and Programming (CS&P 2003)
  • Year:
  • 2003

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Abstract

Communicating Sequential Processes (CSP), is a theoretical framework for discussing concurrent phenomena [7]. In this note, we begin an investigation into the nature of sets of communicating sequential processes. Sets of sequential processes arise naturally when one considers processes contained within specified bounds which provides 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 in this note that basic operators on processes preserve exact sets of processes and they are non-expansive (i.e., non-destructive in terminology of [7]) with respect to the metric D on rough sets [6], [5], restricted to exact sets of processes.