A Polynomial Time Match Test for Large Classes of Extended Regular Expressions

TL;DR

This paper introduces a new automata-based approach to efficiently test matches for large classes of extended regular expressions, transforming an NP-complete problem into polynomial time under certain restrictions.

Contribution

It presents a novel variant of two-way multihead automata that identifies a hidden combinatorial property enabling polynomial time match testing for specific extended regular expressions.

Findings

Polynomial time match test for certain extended regular expressions

Automata-based characterization of match complexity

Extension of results to broader classes is straightforward

Abstract

In the present paper, we study the match test for extended regular expressions. We approach this NP-complete problem by introducing a novel variant of two-way multihead automata, which reveals that the complexity of the match test is determined by a hidden combinatorial property of extended regular expressions, and it shows that a restriction of the corresponding parameter leads to rich classes with a polynomial time match test. For presentational reasons, we use the concept of pattern languages in order to specify extended regular expressions. While this decision, formally, slightly narrows the scope of our results, an extension of our concepts and results to more general notions of extended regular expressions is straightforward.