English

Polynomial Complementation of Nondeterministic 2-Way Finite Automata by 1-Limited Automata

Formal Languages and Automata Theory 2025-07-16 v1

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.

Keywords

Cite

@article{arxiv.2507.11209,
  title  = {Polynomial Complementation of Nondeterministic 2-Way Finite Automata by 1-Limited Automata},
  author = {Bruno Guillon and Luca Prigioniero and Javad Taheri},
  journal= {arXiv preprint arXiv:2507.11209},
  year   = {2025}
}