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Regular expression (regex) matching is fundamental in many applications,especially in web services. However, matching by backtracking -- preferred bymost real-world implementations for its practical performance and backwardcompatibility -- can suffer from so-called catastrophic backtracking, whichmakes the number of backtracking super-linear and leads to the well-known ReDoSvulnerability. Inspired by a recent algorithm by Davis et al. that runs inlinear time for (non-extended) regexes, we study efficient backtrackingmatching for regexes with two common extensions, namely look-around and atomicgrouping. We present linear-time backtracking matching algorithms for theseextended regexes. Their efficiency relies on memoization, much like the one byDavis et al.; we also strive for smaller memoization tables by carefullytrimming their range. Our experiments -- we used some real-world regexes withthe aforementioned extensions -- confirm the performance advantage of ouralgorithms.

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