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Two-dimensional Sgraffito automata∗∗∗

Published online by Cambridge University Press:  06 November 2014

Daniel Průša ,
František Mráz  and
Friedrich Otto
Daniel Průša
Affiliation:
Czech Technical University, Faculty of Electrical Engineering, Karlovo náměstí 13, 12135 Prague 2, Czech Republic.. [email protected]
František Mráz
Affiliation:
Charles University at Prague, Faculty of Mathematics and Physics, Department of Computer Science, Malostranské nám. 25, 11800 Prague 1, Czech Republic. ; [email protected]
Friedrich Otto
Affiliation:
Fachbereich Elektrotechnik/Informatik, Universität Kassel, 34109 Kassel, Germany.; [email protected]
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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.

Keywords

Two-dimensional languageSgraffito automatonbounded Turing machineREC
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 5 , December 2014 , pp. 505 - 539
Copyright
© EDP Sciences 2014

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