Simulating Two-Dimensional Recognizability by Pushdown and Queue Automata

The aim of this paper is to investigate sequential models to describe two-dimensional languages. The intent is to add more capabilities to 4NFA in order to encompass a wider class of languages. We show that any (tiling) recognizable language can be simulated by a 4NFA with an extra queue whose size is bounded by the minimum of the two dimensions of a picture; and that 2NFA (i.e. automata moving only in two directions) with an analogous queue are sufficient when the alphabet is unary. A special class of recognizable languages can be simulated also by 4-way pushdown automata with a stack of size bounded by the sum of the two dimensions of the picture. Such a class is also characterized by a recursive definition involving the operations of union, intersection and a new diagonal overlapping operation applied to languages recognized by 2NFA.