On the complete axiomatization for prefix iteration modulo observation congruence

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. Aceto and Ingólfsdóttir provided an axiom system for observation congruence over basic CCS with prefix iteration. However hitherto the only direct completeness proof given for such a system is very long and technical. In this paper, we provide a new proof for the completeness of the axiom system in [3], which is a considerable simplification comparing to the original proof. Thus the open problem to find a direct completeness proof is closed