An Axiomatization for the Terminal Cycle

Abstract

Milner proposed an axiomatization for the Kleene star in basic process algebra, in the presence of deadlock and empty process, modulo bisimulation equivalence. In this paper, Milner's axioms are adapted to the terminal cycle xω, which executes x infinitely many times in a row, and it is shown that this axiomatization is complete for the terminal cycle in basic process algebra with deadlock and empty process modulo bisimulation.