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.

Process algebra with conditionals in the presence of epsilon

In a previous paper, we presented several extensions of ACP with conditional expressions, including one with a retrospection operator on conditions to allow for looking back on conditions under which preceding actions have been performed. In this paper, we add a constant for a process that is only capable of terminating successfully to those extensions of ACP, which can be very useful in applications. It happens that in all cases the addition of this constant is unproblematic.Comment: 41 page

The cones and foci proof techniques for timed transition systems

We propose an extension of the cones and foci proof technique that can be used to prove timed branching bisimilarity of states in timed transition systems. We prove the correctness of this technique and we give an example verification

On Kleene Algebra vs. Process Algebra

We try to clarify the relationship between Kleene algebra and process algebra, based on the very recent work on Kleene algebra and process algebra. Both for concurrent Kleene algebra (CKA) with communications and truly concurrent process algebra APTC with Kleene star and parallel star, the extended Milner's expansion law $a\parallel b=a\cdot b+b\cdot a+a\parallel b +a\mid b$ holds, with $a,b$ being primitives (atomic actions), $\parallel$ being the parallel composition, $+$ being the alternative composition, $\cdot$ being the sequential composition and the communication merge $\mid$ with the background of computation. CKA and APTC are all the truly concurrent computation models, can have the same syntax (primitives and operators), maybe have the same or different semantics