A proof Procedure for Testing Membership in Regular Expressions

TL;DR

This paper introduces a novel proof-based algorithm for testing membership in regular expressions that avoids automata conversion, making it simpler and adaptable to extended regular language classes.

Contribution

It presents a correct, proof-style membership testing algorithm that extends easily to timed regular expressions and intersections, bypassing automata conversion.

Findings

Algorithm is correct for regular expressions

Avoids complex automata conversion process

Easily extends to extended regular expressions

Abstract

We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the complex conversion process from regular expressions to finite automata is not needed. As a consequence, our algorithm is simple and extends easily to various extensions to regular expressions such as timed regular expressions or regular languages with the intersection.