State Re nement in Process

We introduce a state reenement operator into BPA with recursive speciications and present a comprehensive technical development of the resulting theory, BPA + SR. Our main technical results are that bisimulation is a congruence in BPA+SR and that guarded recursive speciications have unique solutions. We also have that bisimulation remains a congruence if the merge operator of ACP is added to BPA + SR. This is signiicant since action reenement, another approach to reenement in process algebra, does not in general preserve semantic equivalences based on interleavings of atomic actions. State reenement, to our knowledge, represents the rst attempt to capture the essence of Harel's statecharts | viz., hierarchically structured state transition behavior | within a purely process algebraic setting. A succinct, hierarchical speciication of an alarm clock is given to illustrate the utility of state reenement in process algebra.