Finite Automata With Restricted Two-Way Motion

TL;DR

This paper investigates the role of two-way motion in finite automata by measuring left moves, introducing the two-way spectrum, and analyzing how restrictions affect state complexity in accepting regular languages.

Contribution

It introduces the concept of the two-way spectrum, providing bounds and examples, and studies the impact of restrictions on two-way motion on automata state complexity.

Findings

The two-way spectrum varies with the use of two-way motion.

Uniform bounds on automata with restricted two-way motion are established.

Examples demonstrate the sharpness of the bounds.

Abstract

We consider finite two-way automata and measure the use of two-way motion by counting the number of left moves in accepting computations. Restriction of the automata according to this measure allows us to study in detail the use of two-way motion for the acceptance of regular languages in terms of state complexity. The two-way spectrum of a given regular language is introduced. This quantity reflects the change of size of minimal accepting devices if the use of two-way motion is increased incrementally. We give examples for spectra, prove uniform upper and lower bounds and study their sharpness. We also have state complexity results for two-way automata with uniformly bounded use of two-way motion.