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