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

Authors Bruno Guillon , Luca Prigioniero , Javad Taheri

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LIPIcs.STACS.2026.48.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
  • Theory of computation → Models of computation
  • Theory of computation → Regular languages
Keywords
  • descriptional complexity
  • inductive counting
  • common-guess

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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.

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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) https://doi.org/10.4230/LIPIcs.STACS.2026.48

Author Details

Bruno Guillon
  • Université Clermont-Auvergne, CNRS, Mines de Saint-Étienne, Clermont-Auvergne-INP, LIMOS, 63000 Clermont-Ferrand, France
Luca Prigioniero
  • Department of Computer Science, Loughborough University, UK
Javad Taheri
  • Université Clermont-Auvergne, CNRS, Mines de Saint-Étienne, Clermont-Auvergne-INP, LIMOS, 63000 Clermont-Ferrand, France

Acknowledgements

The authors are very grateful to Giovanni Pighizzini for his useful comments and bibliographic help during the writing process.

References

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