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From regular expression matching to parsing

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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, i.e., 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.

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Notes

  1. Sometimes NFAs are allowed a set of accepting states, but this is not necessary for our purposes.

  2. Note that the time bound in the original paper has an additional \(m \log m\) term [4]. Using atomic heaps [9] to represent dictionaries for micro-TNFAs, this term is straightforward to improve to O(m). See also Bille and Thorup [6, Appendix A].

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Acknowledgements

We thank the anonymous reviewers whose comments and suggestions significantly improved the presentation of the paper.

Funding

The funding was provided by Teknologi og Produktion, Det Frie Forskningsråd (Grant No. 4005-00267) and Natur og Univers, Det Frie Forskningsråd (DK) (Grant No. 1323-00178).

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  1. DTU Compute, Technical University of Denmark, 2800, Kgs. Lyngby, Denmark

    Philip Bille & Inge Li Gørtz

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  1. Philip Bille
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  2. Inge Li Gørtz
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Correspondence to Philip Bille.

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An extended abstract appeared at the 44th Mathematical Foundations of Computer Science [5].

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Bille, P., Gørtz, I.L. From regular expression matching to parsing. Acta Informatica 59, 709–724 (2022). https://doi.org/10.1007/s00236-022-00420-6

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