A Cook's Tour of Equational Axiomatizations for Prefix Iteration

Luca Aceto
Willem Jan Fokkink
Anna Ingólfsdóttir

December 1998


Prefix iteration is a variation on the original binary version of the Kleene star operation tex2html_wrap_inline21, obtained by restricting the first argument to be an atomic action, and yields simple iterative behaviours that can be equationally characterized by means of finite collections of axioms. In this paper, we present axiomatic characterizations for a significant fragment of the notions of equivalence and preorder in van Glabbeek's linear-time/branching-time spectrum over Milner's basic CCS extended with prefix iteration. More precisely, we consider ready simulation, simulation, readiness, trace and language semantics, and provide complete (in)equational axiomatizations for each of these notions over BCCS with prefix iteration. All of the axiom systems we present are finite, if so is the set of atomic actions under consideration

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