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Polynomial Complementation of Nondeterministic Two-Way Finite Automata by 1-Limited Automata

Authors: Bruno Guillon, Luca Prigioniero, and Javad Taheri

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)


Abstract
We prove that, paying a polynomial increase in size only, every unrestricted two-way nondeterministic finite automaton (2NFA) can be complemented by a 1-limited automaton (1-LA), a nondeterministic extension of 2NFAs still characterizing regular languages. The resulting machine is actually a restricted form of 1-LAs - known as 2NFAs with common guess - and is self-verifying. A corollary of our construction is that a single exponential is necessary and sufficient for complementing 1-LAs.

Cite as

Bruno Guillon, Luca Prigioniero, and Javad Taheri. Polynomial Complementation of Nondeterministic Two-Way Finite Automata by 1-Limited Automata. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 48:1-48:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)


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@InProceedings{guillon_et_al:LIPIcs.STACS.2026.48,
  author =	{Guillon, Bruno and Prigioniero, Luca and Taheri, Javad},
  title =	{{Polynomial Complementation of Nondeterministic Two-Way Finite Automata by 1-Limited Automata}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{48:1--48:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.48},
  URN =		{urn:nbn:de:0030-drops-255378},
  doi =		{10.4230/LIPIcs.STACS.2026.48},
  annote =	{Keywords: descriptional complexity, inductive counting, common-guess}
}
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