RAIRO-Theor. Inf. Appl.
Volume 48, Number 5, December 2014
|Page(s)||505 - 539|
|Published online||06 November 2014|
1 Czech Technical University, Faculty
of Electrical Engineering, Karlovo náměstí 13, 12135
Prague 2, Czech
2 Charles University at Prague, Faculty of Mathematics and Physics, Department of Computer Science, Malostranské nám. 25, 11800 Prague 1, Czech Republic.
3 Fachbereich Elektrotechnik/Informatik, Universität Kassel, 34109 Kassel, Germany.
Accepted: 28 May 2014
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.
Mathematics Subject Classification: 68Q45
Key words: Two-dimensional language / Sgraffito automaton / bounded Turing machine / REC
This paper summarizes and extends results that have been announced at DLT 2012 in Taipei, August 2012, at DLT 2013 in Paris, June 2013, and at CIAA 2013 in Halifax, July 2013. Extended abstracts appeared in the proceedings of these conferences [18, 20, 21].
© EDP Sciences 2014
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