Search Results

Documents authored by Uezato, Yuya


Document
Track B: Automata, Logic, Semantics, and Theory of Programming
Regular Expressions with Backreferences and Lookaheads Capture NLOG

Authors: Yuya Uezato

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)


Abstract
Backreferences and lookaheads are vital features to make classical regular expressions (REGEX) practical. Although these features have been widely used, understanding of the unrestricted combination of them has been limited. Practically, most likely, no implementation fully supports them. Theoretically, while some studies have addressed these features separately, few have dared to combine them. Those few studies showed that the amalgamation of these features significantly enhances the expressiveness of REGEX. However, no acceptable expressivity bound for REWBLk - REGEX with backreferences and lookaheads - has been established. We elucidate this by establishing that REWBLk coincides with NLOG, the class of languages accepted by log-space nondeterministic Turing machines (NTMs). In translating REWBLk to log-space NTMs, negative lookaheads are the most challenging part since it essentially requires complementing log-space NTMs in nondeterministic log-space. To address this problem, we revisit Immerman-Szelepcsényi theorem. In addition, we employ log-space nested-oracles NTMs to naturally handle nested lookaheads of REWBLk. Utilizing such oracle machines, we also present the new result that the membership problem of REWBLk is PSPACE-complete.

Cite as

Yuya Uezato. Regular Expressions with Backreferences and Lookaheads Capture NLOG. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 155:1-155:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{uezato:LIPIcs.ICALP.2024.155,
  author =	{Uezato, Yuya},
  title =	{{Regular Expressions with Backreferences and Lookaheads Capture NLOG}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{155:1--155:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.155},
  URN =		{urn:nbn:de:0030-drops-202984},
  doi =		{10.4230/LIPIcs.ICALP.2024.155},
  annote =	{Keywords: Regular Expression, Automata Theory, Nondeterministic Log-Space}
}
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail