A note on an expressiveness hierarchy for 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 .. Xn def = PnX1 + Qn where n is a positive integer, and the Pi and the Qi are process terms. The addition of multi-exit iteration to Basic Process Algebra (BPA) yields a more expressive language than that obtained by augmenting BPA with the standard binary Kleene star. This note offers an expressiveness hierarchy, modulo bisimulation equivalence, for the family of multi-exit iteration operators proposed by Bergstra, Bethke and Ponse. AMS Subject Classification (1991): 68Q15, 68Q70. CR Subject Classification (1991): D.3.1, F.1.1, F.4.1.