A Procedure for Checking Equality of Regular Expressions

Abstract

A simple “mechanical” procedure is described for checking equality of regular expressions. The procedure, based on the work of A. Salomaa, uses derivatives of regular expressions and transition graphs. Given a regular expression R , a corresponding transition graph is constructed. It is used to generate a finite set of left-linear equations which characterize R . Two regular events R and S are equal if and only if each constant term in the set of left-linear equations formed for the pair ( R S ) is (φ φ) or (^ ^). The procedure does not involve any computations with or transformations of regular expressions and is especially appropriate for the use of a computer.