From Regular Expression Matching to Parsing

TL;DR

This paper introduces a new technique to convert existing regular expression matching algorithms into algorithms that can also produce detailed match mappings, enabling efficient extraction of subpatterns with linear space complexity.

Contribution

It presents a novel general method for transforming regular expression matching algorithms into parsing algorithms that produce match mappings, achieving linear space efficiency.

Findings

First efficient linear space solutions for regular expression parsing

Enables extraction of subpatterns from matches

Broad applicability to existing algorithms

Abstract

Given a regular expression $R$ and a string $Q$, the regular expression parsing problem is to determine if $Q$ matches $R$ and if so, determine how it matches, e.g., by a mapping of the characters of $Q$ to the characters in $R$. Regular expression parsing makes finding matches of a regular expression even more useful by allowing us to directly extract subpatterns of the match, e.g., for extracting IP-addresses from internet traffic analysis or extracting subparts of genomes from genetic data bases. We present a new general techniques for efficiently converting a large class of algorithms that determine if a string $Q$ matches regular expression $R$ into algorithms that can construct a corresponding mapping. As a consequence, we obtain the first efficient linear space solutions for regular expression parsing.