Two-dimensional Sgraffito automata^∗,∗∗

¹ Czech Technical University, Faculty of Electrical Engineering, Karlovo náměstí 13, 12135 Prague 2, Czech Republic.
prusapa1@cmp.felk.cvut.cz
² Charles University at Prague, Faculty of Mathematics and Physics, Department of Computer Science, Malostranské nám. 25, 11800 Prague 1, Czech Republic.
frantisek.mraz@mff.cuni.cz
³ Fachbereich Elektrotechnik/Informatik, Universität Kassel, 34109 Kassel, Germany.
otto@theory.informatik.uni-kassel.de

Received: 20 December 2013
Accepted: 28 May 2014

Abstract

We present a new model of a two-dimensional computing device called Sgraffito automaton. In general, the model is quite simple, which allows a clear design of computations. When restricted to one-dimensional inputs, that is, strings, the Sgraffito automaton does not exceed the power of finite-state automata. On the other hand, for two-dimensional inputs, it yields a family of picture languages with good closure properties that strictly includes the class REC  of recognizable picture languages. The deterministic Sgraffito automata define a class of picture languages that includes the class of deterministic recognizable picture languages DREC, the class of picture languages that are accepted by four-way alternating automata, those that are accepted by deterministic one-marker automata, and the sudoku-deterministically recognizable picture languages, but the membership problem for the accepted languages is still decidable in polynomial time. In addition, the deterministic Sgraffito automata accept some unary picture languages that are outside of the class REC.