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Multiset, Set and Numerically Decipherable Codes over Directed Figures

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Combinatorial Algorithms (IWOCA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7643))

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Abstract

Codes with various kinds of decipherability, weaker than the usual unique decipherability, have been studied since multiset decipherability was introduced in mid-1980s. We consider decipherability of directed figure codes, where directed figures are defined as labelled polyominoes with designated start and end points, equipped with catenation operation that may use a merging function to resolve possible conflicts. This is one of possible extensions generalizing words and variable-length codes to planar structures.

Here, verification whether a given set is a code is no longer decidable in general. We study the decidability status of figure codes depending on catenation type (with or without a merging function), decipherability kind (unique, multiset, set or numeric) and code geometry (several classes determined by relative positions of start and end points of figures). We give decidability or undecidability proofs in all but two cases that remain open.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348, Kraków, Poland

    Michał Kolarz & Włodzimierz Moczurad

Authors
  1. Michał Kolarz
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  2. Włodzimierz Moczurad
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Editor information

Editors and Affiliations

  1. Kalasalingam University, Anand Nagar, 626 126, Krishanakoil, Tamil Nadu, India

    S. Arumugam

  2. Algorithms Research Group, Department of Computing & Software, McMaster University, L8S 4K1, Hamilton, ON, Canada

    W. F. Smyth

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Kolarz, M., Moczurad, W. (2012). Multiset, Set and Numerically Decipherable Codes over Directed Figures. In: Arumugam, S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2012. Lecture Notes in Computer Science, vol 7643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35926-2_25

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  • DOI: https://doi.org/10.1007/978-3-642-35926-2_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35925-5

  • Online ISBN: 978-3-642-35926-2

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