The equational theory of prebisimilarity over basic CCS with divergence

This paper studies the equational theory of prebisimilarity, a bisimulation-based preorder introduced by Hennessy and Milner in the early 1980s, over basic CCS with the divergent process Ω. It is well known that prebisimilarity affords a finite ground-complete axiomatization over this language; this study proves that this ground-complete axiomatization is also complete in the presence of an infinite set of actions. Moreover, in sharp contrast to this positive result, it is shown that prebisimilarity is not finitely based over basic CCS with the divergent process Ω when the set of actions is finite and nonempty.