An equational axiomatization of bisimulation over regular expressions
We provide a finite equational axiomatization for bisimulation equivalence of nondeterministic interpretation of regular expressions. Our axiomatization is heavily based on the one by Salomaa, that provided an implicative axiomatization for a large subset of regular expressions, namely all those that satisfy the non-empty word property (i.e. without 1 summands at the top level) in *-contexts. Our restriction is similar, it essentially amounts to recursively requiring that the non-empty word property be satisfied not just at top level but at any depth. We also discuss the impact on the axiomatization of different interpretations of the 0 term, interpreted either as a null process or as a deadlock.
equational axiomatization bisimulation regular expressions concurency nondeterminism process algebras