Branching bisimilarity is an equivalence indeed!
Information Processing Letters
Branching time and abstraction in bisimulation semantics
Journal of the ACM (JACM)
Rooted branching bisimulation as a congruence
Journal of Computer and System Sciences
The cones and foci proof technique for timed transition systems
Information Processing Letters
Communication and Concurrency
Process Algebra with Timing
CONCUR '92 Proceedings of the Third International Conference on Concurrency Theory
Abstraction in Real Time Process Algebra
Proceedings of the Real-Time: Theory in Practice, REX Workshop
Action abstraction in timed process algebra: the case for an untimed silent step
FSEN'07 Proceedings of the 2007 international conference on Fundamentals of software engineering
Is timed branching bisimilarity an equivalence indeed?
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
Fundamenta Informaticae
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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.