Two-Dimensional Typewriter Automata

TL;DR

This paper introduces the typewriter automaton, a new two-dimensional automaton model with unique movement constraints, and explores its recognition capabilities, closure properties, and complexity bounds.

Contribution

It initiates the study of the typewriter automaton model, relating it to existing models and analyzing its recognition power and operational complexity.

Findings

Established closure properties of the recognized language class

Analyzed state complexity bounds for row concatenation

Compared the model with similar two-dimensional automata

Abstract

A typewriter automaton is a special variant of a two-dimensional automaton that receives two-dimensional words as input and is only capable of moving its input head through its input word in three directions: downward, leftward, and rightward. In addition, downward and leftward moves may only be made via a special "reset" move that simulates the action of a typewriter's carriage return. In this paper, we initiate the study of the typewriter automaton model and relate it to similar models, including three-way two-dimensional automata, boustrophedon automata, and returning automata. We study the recognition powers of the typewriter automaton model, establish closure properties of the class of languages recognized by the model, and consider operational state complexity bounds for the specific operation of row concatenation. We also provide a variety of potential future research directions pertaining to the model.