Axiomatizing Prefix Iteration with Silent Steps

Luca Aceto
Wan J. Fokkink
Rob J. van Glabbeek
Anna Ingólfsdóttir

November 1995


Prefix iteration is a variation on the original binary version of the Kleene star operation tex2html_wrap_inline19 , obtained by restricting the first argument to be an atomic action. The interaction of prefix iteration with silent steps is studied in the setting of Milner's basic CCS. Complete equational axiomatizations are given for four notions of behavioural congruence overbasic CCS with prefix iteration, viz. branching congruence, tex2html_wrap_inline21 -congruence, delay congruence and weak congruence. The completeness proofs for tex2html_wrap_inline21 -, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence. It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature. The preliminaries and the completeness proofs focus on open terms, i.e., terms that may contain process variables. As a byproduct, the tex2html_wrap_inline25 -completeness of the axiomatizations is obtained as well as their completeness for closed terms.

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