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Picture Codes with Finite Deciphering Delay

  • Marcella Anselmo
  • Dora Giammarresi
  • Maria Madonia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)

Abstract

A two-dimensional code is defined as a set X ⊆ Σ** such that any picture over Σ is tilable in at most one way with pictures in X. The codicity problem is in general undecidable. Very recently in [4] prefix picture codes were introduced as a decidable subclass that generalizes prefix string codes. Finite deciphering delay sets are an interesting class of string codes that coincide with prefix codes in the case of delay equal to 0. An analogous notion is introduced for picture codes and it is proved that they correspond to a bigger class of decidable picture codes that includes interesting examples and special cases.

Keywords

Two-dimensional languages codes 

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References

  1. 1.
    Aigrain, P., Beauquier, D.: Polyomino tilings, cellular automata and codicity. Theoretical Computer Science 147, 165–180 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Anselmo, M., Giammarresi, D., Madonia, M.: Deterministic and unambiguous families within recognizable two-dimensional languages. Fund. Inform 98(2-3), 143–166 (2010)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Anselmo, M., Giammarresi, D., Madonia, M.: Strong prefix codes of pictures. In: Muntean, T., Poulakis, D., Rolland, R. (eds.) CAI 2013. LNCS, vol. 8080, pp. 47–59. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  4. 4.
    Anselmo, M., Giammarresi, D., Madonia, M.: Two-dimensional codes of pictures. In: Béal, M.-P., Carton, O. (eds.) DLT 2013. LNCS, vol. 7907, pp. 46–57. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Anselmo, M., Giammarresi, D., Madonia, M., Restivo, A.: Unambiguous recognizable two-dimensional languages. RAIRO: Theoretical Informatics and Applications 40(2), 227–294 (2006)MathSciNetGoogle Scholar
  6. 6.
    Anselmo, M., Madonia, M.: Deterministic and unambiguous two-dimensional languages over one-letter alphabet. Theoretical Computer Science 410(16), 1477–1485 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Beauquier, D., Nivat, M.: A codicity undecidable problem in the plane. Theoret. Comp. Sci. 303, 417–430 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Berstel, J., Perrin, D., Reutenauer, C.: Codes and Automata. Cambridge University Press (2009)Google Scholar
  9. 9.
    Bozapalidis, S., Grammatikopoulou, A.: Picture codes. ITA 40(4), 537–550 (2006)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Bruyère, V., Wang, L., Zhang, L.: On completion of codes with finite deciphering delay. Europ. J. Combinatorics 11, 513–521 (1990)CrossRefzbMATHGoogle Scholar
  11. 11.
    Giammarresi, D., Restivo, A.: Recognizable picture languages. Int. Journal Pattern Recognition and Artificial Intelligence 6(2-3), 241–256 (1992)CrossRefGoogle Scholar
  12. 12.
    Giammarresi, D., Restivo, A.: Two-dimensional languages. In: Rozenberg, G. (ed.) Handbook of Formal Languages, vol. III, pp. 215–268. Springer (1997)Google Scholar
  13. 13.
    Grammatikopoulou, A.: Prefix picture sets and picture codes. In: Procs. CAI 2005, pp. 255–268. Aristotle University of Thessaloniki (2005)Google Scholar
  14. 14.
    Kolarz, M., Moczurad, W.: Multiset, Set and Numerically Decipherable Codes over Directed Figures. In: Smyth, B. (ed.) IWOCA 2012. LNCS, vol. 7643, pp. 224–235. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  15. 15.
    Lindgren, K., Moore, C., Nordahl, M.: Complexity of two-dimensional patterns. Journal of Statistical Physics 91(5-6), 909–951 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Moczurad, M., Moczurad, W.: Some open problems in decidability of brick (Labelled polyomino) codes. In: Chwa, K.-Y., Munro, J.I. (eds.) COCOON 2004. LNCS, vol. 3106, pp. 72–81. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Simplot, D.: A characterization of recognizable picture languages by tilings by finite sets. Theoretical Computer Science 218(2), 297–323 (1991)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Marcella Anselmo
    • 1
  • Dora Giammarresi
    • 2
  • Maria Madonia
    • 3
  1. 1.Dipartimento di InformaticaUniversità di SalernoFiscianoItaly
  2. 2.Dipartimento di MatematicaUniversità Roma “Tor Vergata”RomaItaly
  3. 3.Dipartimento di Matematica e InformaticaUniversità di CataniaCataniaItaly

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