Two-Dimensional Typewriter 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.