Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata
Abstract
The row projection (resp., column projection) of a two-dimensional language is the one-dimensional language consisting of all first rows (resp., first columns) of each two-dimensional word in . The operation of row projection has previously been studied under the name "frontier language", and previous work has focused on one- and two-dimensional language classes. In this paper, we study projections of languages recognized by various two-dimensional automaton classes. We show that both the row and column projections of languages recognized by (four-way) two-dimensional automata are exactly context-sensitive. We also show that the column projections of languages recognized by unary three-way two-dimensional automata can be recognized using nondeterministic logspace. Finally, we study the state complexity of projection languages for two-way two-dimensional automata, focusing on the language operations of union and diagonal concatenation.
Keywords
Cite
@article{arxiv.2009.00602,
title = {Recognition and Complexity Results for Projection Languages of Two-Dimensional Automata},
author = {Taylor J. Smith and Kai Salomaa},
journal= {arXiv preprint arXiv:2009.00602},
year = {2020}
}