Is Timed Branching Bisimilarity a Congruence Indeed?
Wan Fokkink, Jun Pang, and Anton Wijs
Fundamenta Informaticae XX:1-25, 2008
We show that timed branching bisimilarity as defined by Van der Zwaag  and Baeten and Middelburg  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.