A Complete Equational Axiomatization for BPAdelta epsilon with Prefix Iteration (original) (raw)

Prefix iteration x is added to Basic Process Algebra with deadlock and empty process. We present a finite equational axiomatization for this process algebra, and we prove that this axiomatization is complete with respect to strong bisimulation equivalence. This result is a mild generalization of a similar result in the setting of basic CCS in Fokkink (1994b). To obtain this completeness result, we set up a rewrite system, based on the axioms. In order to prove that this rewrite system is terminating modulo AC of the +, we generalize a termination theorem from Zantema and Geser (1994) to the setting of rewriting modulo equations. Finally, we show that bisimilar normal forms are syntactically equal modulo AC of the +. 1 Introduction Kleene (1956) defined a binary operator in the context of finite automata, called Kleene star or iteration. Intuitively, the expression p q yields a solution for the recursive equation X = p Delta X + q. In other words, p q can choose to execut...