Efficient Matching with Memoization for Regexes with Look-around and Atomic Grouping (Extended Version)

TL;DR

This paper introduces linear-time backtracking algorithms for extended regexes with look-around and atomic grouping, using optimized memoization to prevent catastrophic backtracking and improve performance in real-world applications.

Contribution

It extends Davis et al.'s linear-time regex matching algorithm to handle look-around and atomic groups with optimized memoization strategies.

Findings

Algorithms achieve linear-time matching for extended regexes.

Experiments show significant performance improvements over traditional backtracking.

Memoization table optimization reduces memory usage without sacrificing speed.

Abstract

Regular expression (regex) matching is fundamental in many applications, especially in web services. However, matching by backtracking -- preferred by most real-world implementations for its practical performance and backward compatibility -- can suffer from so-called catastrophic backtracking, which makes the number of backtracking super-linear and leads to the well-known ReDoS vulnerability. Inspired by a recent algorithm by Davis et al. that runs in linear time for (non-extended) regexes, we study efficient backtracking matching for regexes with two common extensions, namely look-around and atomic grouping. We present linear-time backtracking matching algorithms for these extended regexes. Their efficiency relies on memoization, much like the one by Davis et al.; we also strive for smaller memoization tables by carefully trimming their range. Our experiments -- we used some real-world regexes with the aforementioned extensions -- confirm the performance advantage of our algorithms.