Fine-Grained Complexity of Regular Expression Pattern Matching and Membership

Philipp Schepper

doi:10.4230/lipics.esa.2020.80

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arXiv · 2008.02769

Fine-Grained Complexity of Regular Expression Pattern Matching and Membership

Philipp Schepper

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Abstract

The currently fastest algorithm for regular expression pattern matching and membership improves the classical O(nm) time algorithm by a factor of about log^{3/2}n. Instead of focussing on general patterns we analyse homogeneous patterns of bounded depth in this work. For them a classification splitting the types in easy (strongly sub-quadratic) and hard (essentially quadratic time under SETH) is known. We take a very fine-grained look at the hard pattern types from this classification and show a dichotomy: few types allow super-poly-logarithmic improvements while the algorithms for the other pattern types can only be improved by a constant number of log-factors, assuming the Formula-SAT Hypothesis.

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Philipp Schepper. 2020-08-06. Fine-Grained Complexity of Regular Expression Pattern Matching and Membership. https://doi.org/10.4230/lipics.esa.2020.80

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