6 research outputs found
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 solutionsof systems of recursion equations of the formX1 = P1 X2 + Q1...Xn = Pn X1 + Qnwhere n is a positive integer, and the Pi and the Qi are process terms. The additionof multi-exit iteration to BPA yields a more expressive language than that obtained by augmenting BPA with the standard binary Kleene star (BPA). As aconsequence, the proof of completeness of the proposed equational axiomatizationfor this language, although standard in its general structure, is much more involvedthan that for BPA. An expressiveness hierarchy for the family of k-exit iteration operators proposed by Bergstra, Bethke and Ponse is also offered.
A Complete Proof System for 1-Free Regular Expressions Modulo Bisimilarity
Robin Milner (1984) gave a sound proof system for bisimilarity of regular
expressions interpreted as processes: Basic Process Algebra with unary Kleene
star iteration, deadlock 0, successful termination 1, and a fixed-point rule.
He asked whether this system is complete. Despite intensive research over the
last 35 years, the problem is still open.
This paper gives a partial positive answer to Milner's problem. We prove that
the adaptation of Milner's system over the subclass of regular expressions that
arises by dropping the constant 1, and by changing to binary Kleene star
iteration is complete. The crucial tool we use is a graph structure property
that guarantees expressibility of a process graph by a regular expression, and
is preserved by going over from a process graph to its bisimulation collapse