Converting Nondeterministic Two-Way Automata into Small Deterministic Linear-Time Machines

TL;DR

This paper introduces a new method to convert nondeterministic two-way automata into small, linear-time deterministic machines with only polynomial size increase, advancing understanding of automata transformation costs.

Contribution

It presents a novel approach for simulating nondeterministic finite automata with deterministic models in linear time, reducing the size blow-up from exponential to polynomial.

Findings

Polynomial size increase in automata conversion

Simulation of nondeterministic automata by linear-time deterministic machines

Equivalent computational power to regular languages

Abstract

In 1978 Sakoda and Sipser raised the question of the cost, in terms of size of representations, of the transformation of two-way and one-way nondeterministic automata into equivalent two-way deterministic automata. Despite all the attempts, the question has been answered only for particular cases (e.g., restrictions of the class of simulated automata or of the class of simulating automata). However the problem remains open in the general case, the best-known upper bound being exponential. We present a new approach in which unrestricted nondeterministic finite automata are simulated by deterministic models extending two-way deterministic finite automata, paying a polynomial increase of size only. Indeed, we study the costs of the conversions of nondeterministic finite automata into some variants of one-tape deterministic Turing machines working in linear time, namely Hennie machines, weight-reducing Turing machines, and weight-reducing Hennie machines. All these variants are known to share the same computational power: they characterize the class of regular languages.