The algebra of communicating processes with empty process

AbstractThe axiom systems BPAε, BPAεδ, PAε and ACPε which are in essence the systems BPA, PA and ACP extended with the empty process are presented. For the system ACPε, that contains the other three systems, the first steps are taken towards making it operational: the most basic supplementary axioms are given. It is also adapted such that they can deal with the empty process and a graph model is constructed. The validity of the supplementary axioms is proven in both the closed term model and the graph model