Is Timed Branching Bisimilarity a Congruence Indeed?

Article type: Research Article

Authors: Fokkink, Wan | Pang, Jun | Wijs, Anton

Affiliations: Department of Computer Science Vrije Universiteit, Amsterdam & Department of Software Engineering, CWI, Amsterdam, The Netherlands. [email protected] | Faculté des Sciences, de la Technologie et de la Communication Université du Luxembourg, France. [email protected] | Faculté des Sciences Mirande INRIA / VASY, Dijon, France. [email protected]

Note: [] Address for correspondence: Vrije Universiteit Amsterdam, Department of Computer Science, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands. [email protected]

Abstract: We show that timed branching bisimilarity as defined by Van der Zwaag [17] and Baeten and Middelburg [2] is not an equivalence relation, in case of a dense time domain. We propose an adaptation based on Van der Zwaag's definition, and prove that the resulting timed branching bisimilarity is an equivalence indeed. Furthermore, we prove that in case of a discrete time domain, Van der Zwaag's definition and our adaptation coincide. Finally, we prove that a rooted version of timed branching bisimilarity is a congruence over a basic timed process algebra containing parallelism, successful termination and deadlock.

Journal: Fundamenta Informaticae, vol. 87, no. 3-4, pp. 287-311, 2008