A Complete Equational Axiomatization for Prefix Iteration with Silent Steps

Abstract

Fokkink ((1994) Inf. Process. Lett. 52: 333{337) has recently proposed a complete
equational axiomatization of strong bisimulation equivalence for MPA_delta^*(A_tau),
i.e., the language obtained by extending Milner's basic CCS with prefix iteration.
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. In this
paper, we extend Fokkink's results to a setting with the unobservable action by
giving a complete equational axiomatization of Milner's observation congruence over
MPA_delta^*(A_tau ).
The axiomatization is obtained by extending Fokkink's axiom system
with two of Milner's standard tau-laws and the following three equations that describe
the interplay between the silent nature of tau and prefix iteration:
tau . x = tau*x
a*(x+tau.y) = a*(x+tau.y + a.y)
tau.(a*x) = a*(tau.a*x) .
Using a technique due to Groote, we also show that the resulting axiomatization is
omega-complete, i.e., complete for equality of open terms.
AMS Subject Classification (1991): 68Q40, 68Q42.
CR Subject Classification (1991): D.3.1, F.3.2, F.4.2.
Keywords and Phrases: Minimal Process Algebra, prefix iteration, equational
logic, omega-completeness, observation congruence.