Abstract
We consider directed figures defined as labelled polyominoes with designated start and end points, equipped with catenation operation that uses a merging function to resolve possible conflicts. This is one of possible extensions generalizing words and variable-length codes to planar structures, creating a new tool for e.g. image analysis and retrieval.
Within this model, we define four kinds of codes that differ in their treatment of start and end points. This is a generalization that weakens (one or both of) equality tests in the classical definition of a code. We show a strict hierarchy of those kinds and prove that testing whether a given set of figures is a code of a given kind is decidable. This is an extension of previous results, leading to a verification algorithm for codes of all four kinds.
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References
Aigrain, P., Beauquier, D.: Polyomino tilings, cellular automata and codicity. Theoretical Computer Science 147(1-2), 165–180 (1995)
Beauquier, D., Nivat, M.: A codicity undecidable problem in the plane. Theoretical Computer Science 303(2-3), 417–430 (2003)
Costagliola, G., Ferrucci, F., Gravino, C.: Adding symbolic information to picture models: definitions and properties. Theoretical Computer Science 337, 51–104 (2005)
Giammarresi, D., Restivo, A.: Two-dimensional finite state recognizability. Fundamenta Informaticae 25(3), 399–422 (1996)
Halava, V., Harju, T., Kärki, T.: Relational codes of words. Theoretical Computer Science 389(1-2), 237–249 (2007)
Kolarz, M.: Directed figures: extended models. Theoretical Informatics and Applications RAIRO (submitted), http://www.ii.uj.edu.pl/~kolarz/ita09010.pdf
Kolarz, M., Moczurad, W.: Directed figure codes are decidable. Discrete Mathematics and Theoretical Computer Science 11(2), 1–14 (2009)
Mantaci, S., Restivo, A.: Codes and equations on trees. Theoretical Computer Science 255, 483–509 (2001)
Moczurad, W.: Brick codes: families, properties, relations. International Journal of Computer Mathematics 74, 133–150 (2000)
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Moczurad, W. (2010). Directed Figure Codes with Weak Equality. In: Fyfe, C., Tino, P., Charles, D., Garcia-Osorio, C., Yin, H. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2010. IDEAL 2010. Lecture Notes in Computer Science, vol 6283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15381-5_30
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DOI: https://doi.org/10.1007/978-3-642-15381-5_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15380-8
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