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

TL;DR

This paper demonstrates that nondeterministic 2-way finite automata can be polynomially complemented by a restricted form of 1-limited automata, establishing a new method for automaton complementation with size efficiency.

Contribution

It introduces a polynomial-size complementation construction for 2NFA using 1-LA variants, advancing understanding of automaton transformations.

Findings

Polynomial size increase for complementation

Equivalence of 1-LA extension and regular languages

Single exponential bound for complementing 1-LAs

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.