4 research outputs found
A Complete Proof System for 1-Free Regular Expressions Modulo Bisimilarity
Robin Milner (1984) gave a sound proof system for bisimilarity of regular
expressions interpreted as processes: Basic Process Algebra with unary Kleene
star iteration, deadlock 0, successful termination 1, and a fixed-point rule.
He asked whether this system is complete. Despite intensive research over the
last 35 years, the problem is still open.
This paper gives a partial positive answer to Milner's problem. We prove that
the adaptation of Milner's system over the subclass of regular expressions that
arises by dropping the constant 1, and by changing to binary Kleene star
iteration is complete. The crucial tool we use is a graph structure property
that guarantees expressibility of a process graph by a regular expression, and
is preserved by going over from a process graph to its bisimulation collapse
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 nonâempty word property (i.e. without 1 summands at the top level) in *âcontexts. Our restriction is similar, it essentially amounts to recursively requiring that the nonâempty 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