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Ordered Restarting Automata for Picture Languages

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SOFSEM 2014: Theory and Practice of Computer Science (SOFSEM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8327))

Abstract

We introduce a two-dimensional variant of the restarting automaton with window size three-by-three for processing rectangular pictures. In each rewrite step such an automaton can only replace the symbol in the middle position of its window by a symbol that is smaller with respect to a fixed ordering on the tape alphabet. When restricted to one-dimensional inputs (that is, words) the deterministic variant of these ordered restarting automata only accepts regular languages, while the nondeterministic one can accept some languages that are not even context-free. We then concentrate on the deterministic two-dimensional ordered restarting automaton, showing that it is quite expressive as it can simulate the deterministic sgraffito automaton, and we present some closure and non-closure properties for the class of picture languages accepted by these automata.

The first author was supported by the Grant Agency of the Czech Republic under the project P103/10/0783.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 118 25, Prague 1, Czech Republic

    František Mráz

  2. Fachbereich Elektrotechnik/Informatik, Universität Kassel, 34109, Kassel, Germany

    Friedrich Otto

Authors
  1. František Mráz
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  2. Friedrich Otto
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Editor information

Editors and Affiliations

  1. Dep. Computer Sci., P. J. Šafárik University, Jesenná 5, 04154, Košice, Slovakia

    Viliam Geffert

  2. Katholieke Universiteit Leuven, 3001, Leuven-Heverlee, Belgium

    Bart Preneel

  3. Department of Computer Science, Comenius University, Mlynska Dolina, 84248, Bratislava, Slovakia

    Branislav Rovan

  4. Institute of Computer Science, Academy of Sciences, 18207, Prague, Czech Republic

    Július Štuller

  5. Institute of Software Technology, Vienna University of Technology, Favoritenstraße 9-11 / 188, 1040, Vienna, Austria

    A Min Tjoa

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© 2014 Springer International Publishing Switzerland

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Mráz, F., Otto, F. (2014). Ordered Restarting Automata for Picture Languages. In: Geffert, V., Preneel, B., Rovan, B., Štuller, J., Tjoa, A.M. (eds) SOFSEM 2014: Theory and Practice of Computer Science. SOFSEM 2014. Lecture Notes in Computer Science, vol 8327. Springer, Cham. https://doi.org/10.1007/978-3-319-04298-5_38

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  • DOI: https://doi.org/10.1007/978-3-319-04298-5_38

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-04297-8

  • Online ISBN: 978-3-319-04298-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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