A Complete Axiomatisation for Divergence Preserving Branching Congruence of Finite-State Behaviours

We present an equational inference system for finite-state expressions, and prove that the system is sound and complete with respect to divergence preserving branching congruence, closing a problem that has been open since 1993. The inference system refines Rob van Glabbeek’s simple and elegant complete axiomatisation for branching bisimulation congruence of finite-state behaviours by joining four simple axioms after dropping one axiom which is unsound under the more refined divergence sensitive semantics.