Snake-Deterministic Tiling Systems

  • Violetta Lonati
  • Matteo Pradella
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5734)

Abstract

The concept of determinism, while clear and well assessed for string languages, is still matter of research as far as picture languages are concerned. We introduce here a new kind of determinism, called snake, based on the boustrophedonic scanning strategy, that is a natural scanning strategy used by many algorithms on 2D arrays and pictures. We consider a snake-deterministic variant of tiling systems, which defines the so-called Snake-DREC class of languages. Snake-DREC properly extends the more traditional approach of diagonal-based determinism, used e.g. by deterministic tiling systems, and by online tessellation automata. Our main result is showing that the concept of snake-determinism of tiles coincides with row (or column) unambiguity.

Keywords

picture language 2D language tiling systems online tessellation automata determinism unambiguity 

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References

  1. 1.
    Anselmo, M., Giammarresi, D., Madonia, M.: From determinism to non-determinism in recognizable two-dimensional languages. In: Harju, T., Karhumäki, J., Lepistö, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 36–47. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  2. 2.
    Anselmo, M., Giammarresi, D., Madonia, M.: A computational model for recognizable two-dimensional languages. Theoretical Computer Science (to appear, 2009)Google Scholar
  3. 3.
    Anselmo, M., Giammarresi, D., Madonia, M., Restivo, A.: Unambiguous recognizable two-dimensional languages. Theoretical Informatics and Applications 40(2), 277–293 (2006)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Behrooz, P.: Introduction to Parallel Processing: Algorithms and Architectures. Kluwer Academic Publishers, Norwell (1999)Google Scholar
  5. 5.
    Bertoni, A., Goldwurm, M., Lonati, V.: On the complexity of unary tiling-recognizable picture languages. Fundamenta Informaticae 91(2), 231–249 (2009)MathSciNetMATHGoogle Scholar
  6. 6.
    Cherubini, A., Crespi Reghizzi, S., Pradella, M.: Regional languages and tiling: A unifying approach to picture grammars. In: Ochmański, E., Tyszkiewicz, J. (eds.) MFCS 2008. LNCS, vol. 5162, pp. 253–264. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Giammarresi, D., Restivo, A.: Recognizable picture languages. International Journal Pattern Recognition and Artificial Intelligence 6(2-3), 241–256 (1992); Special Issue on Parallel Image ProcessingCrossRefMATHGoogle Scholar
  8. 8.
    Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Salomaa, A., Rozenberg, G. (eds.) Handbook of Formal Languages. Beyond Words, vol. 3, pp. 215–267. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  9. 9.
    Inoue, K., Nakamura, A.: Some properties of two-dimensional on-line tessellation acceptors. Information Sciences 13, 95–121 (1977)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Inoue, K., Takanami, I.: A survey of two-dimensional automata theory. Information Sciences 55(1-3), 99–121 (1991)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Lindgren, K., Moore, C., Nordahl, M.: Complexity of two-dimensional patterns. Journal of Statistical Physics 91(5-6), 909–951 (1998)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Matz, O.: On piecewise testable, starfree, and recognizable picture languages. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, pp. 203–210. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Violetta Lonati
    • 1
  • Matteo Pradella
    • 2
  1. 1.Dipartimento di Scienze dell’InformazioneUniversità degli Studi di MilanoMilanoItaly
  2. 2.IEIIT, Consiglio Nazionale delle RicercheMilanoItaly

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