New results on deterministic sgraffito automata

Abstract

The deterministic sgraffito automaton is a two-dimensional computing device that allows a clear and simple design of important computations. The family of picture languages it accepts has many nice closure properties, but when restricted to one-row inputs (that is, strings), this family collapses to the class of regular languages. Here we compare the deterministic sgraffito automaton to some other two-dimensional models: the two-dimensional deterministic forgetting automaton, the four-way alternating automaton and the sudoku-deterministically recognizable picture languages. In addition, we prove that deterministic sgraffito automata accept some unary picture languages that are outside the class REC of recognizable picture languages. © 2013 Springer-Verlag.