Axiomatizing Prefix Iteration with Silent Steps

L. Aceto, W.J. Fokkink, R.J. van Glabbeek, A. Ingólfsdóttir

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Prefix iteration is a variation on the original binary version of the Kleene star operationP*Q, 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 over basic CCS with prefix iteration, viz., branching congruence,η-congruence, delay congruence, and weak congruence. The completeness proofs forη-, 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 by-product, theω-completeness of the axiomatizations is obtained, as well as their completeness for closed terms.

Original languageEnglish
Pages (from-to)26-40
Number of pages15
JournalInformation and Computation
Issue number1
Publication statusPublished - 5 May 1996


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