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Two Dimensional Prefix Codes of Pictures

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Developments in Language Theory (DLT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7907))

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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 undecidable. The subclass of prefix codes is introduced and it is proved that it is decidable whether a finite set of pictures is a prefix code. Further a polynomial time decoding algorithm for finite prefix codes is given. Maximality and completeness of finite prefix codes are studied: differently from the one-dimensional case, they are not equivalent notions. Completeness of finite prefix codes is characterized.

Partially supported by MIUR Project “Aspetti matematici e applicazioni emergenti degli automi e dei linguaggi formali”, by 60 % Projects of University of Catania, Roma “Tor Vergata”, Salerno.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Salerno, I-84084, Fisciano, SA, Italy

    Marcella Anselmo

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata”, via della Ricerca Scientifica, 00133, Roma, Italy

    Dora Giammarresi

  3. Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6/a, 95125, Catania, Italy

    Maria Madonia

Authors
  1. Marcella Anselmo
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  2. Dora Giammarresi
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  3. Maria Madonia
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Editor information

Editors and Affiliations

  1. LIGM, University Paris-Est Marne-la-Vallée, 5 Bd Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée Cedex 2, France

    Marie-Pierre Béal

  2. LIAFA, UMR 7089, University Paris Diderot, 75205, Paris cedex 13, France

    Olivier Carton

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Anselmo, M., Giammarresi, D., Madonia, M. (2013). Two Dimensional Prefix Codes of Pictures. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_6

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  • DOI: https://doi.org/10.1007/978-3-642-38771-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38770-8

  • Online ISBN: 978-3-642-38771-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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