Degrees of Restriction for Two-Dimensional Automata
Abstract
A three-way (resp., two-way) two-dimensional automaton has a read-only input head that moves in three (resp., two) directions on a finite array of cells labelled by symbols of the input alphabet. Restricting the input head movement of a two-dimensional automaton results in a model that is weaker in terms of recognition power. In this paper, we introduce the notion of "degrees of restriction" for two-dimensional automata, and we develop sets of extended two-dimensional automaton models that allow for some bounded number of restricted moves. We establish recognition hierarchies for both deterministic and nondeterministic extended three-way two-dimensional automata, and we find similar hierarchies for both deterministic and nondeterministic extended two-way two-dimensional automata. We also prove incomparability results between nondeterministic and deterministic extended three-way two-dimensional automata. Lastly, we consider closure properties for some operations on languages recognized by extended three-way two-dimensional automata.
Keywords
Cite
@article{arxiv.2105.01179,
title = {Degrees of Restriction for Two-Dimensional Automata},
author = {Taylor J. Smith and Kai Salomaa},
journal= {arXiv preprint arXiv:2105.01179},
year = {2021}
}