Open AccessAxiomatizing Prefix Iteration with Silent Steps
Author(s) -
Luca Aceto,
Willem Jan Fokkink,
Rob J. van Glabbeek,
Anna Ingólfsdóttir
Publication year - 1995
Publication title -
brics report series
Language(s) - English
Resource type - Journals
eISSN - 1601-5355
pISSN - 0909-0878
DOI - 10.7146/brics.v2i56.19957
Subject(s) - mathematics , congruence (geometry) , bisimulation , mathematical proof , prefix , discrete mathematics , gödel's completeness theorem , concurrency , completeness (order theory) , combinatorics , algebra over a field , pure mathematics , computer science , mathematical analysis , philosophy , linguistics , geometry , operating system
Prefix iteration is a variation on the original binary version of the Kleene star operation P*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, eta-congruence, delay congruence and weak congruence. The completeness proofs for eta-, 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, the omega-completeness of the axiomatizations is obtained as well as their completeness for closed terms. AMS Subject Classification (1991): 68Q10, 68Q40, 68Q55. CR Subject Classification (1991): D.3.1, F.1.2, F.3.2. Keywords and Phrases: Concurrency, process algebra, basic CCS, prefix iteration, branching bisimulation, eta-bisimulation, delay bisimulation, weak bisimulation, equational logic, complete axiomatizations.