An Equational Axiomatization for Multi-exit Iteration

This paper presents an equational axiomatization of bisimulation equivalence over the language of Basic Process Algebra (BPA) with multi-exit iteration. Multi-exit iteration is a generalization of the standard binary Kleene star operation that allows for the specification of agents that, up to bisimulation equivalence, are solutions of systems of recursion equations of the form X₁ =^def P₁X₂ + Q₁ ⋮ X_n =^def P_nX₁ + Q_n, where n is a positive integer and the P_i and the Q_i are process terms. The addition of multi-exit iteration to BPA yields a more expressive language than that obtained by augmenting BPA with the standard binary Kleene star (BPA*). As a consequence, the proof of completeness of the proposed equational axiomatization for this language, although standard in its general structure, is much more involved than that for BPA*. An expressiveness hierarchy for the family of k-exit iteration operators proposed by Bergstra, Bethke, and Ponse is also offered.