Michal Kolarz ; Wlodzimierz Moczurad - Directed figure codes are decidable

dmtcs:455 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, Vol. 11 no. 2 - https://doi.org/10.46298/dmtcs.455
Directed figure codes are decidable

Authors: Michal Kolarz ; Wlodzimierz Moczurad

    Two-dimensional structures of various kinds can be viewed as generalizations of words. Codicity verification and the defect effect, important properties related to word codes, are studied also in this context. Unfortunately, both are lost in the case of two common structures, polyominoes and figures. 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. We prove that in this setting verification whether a given finite set of directed figures is a code is decidable and we give a constructive algorithm. We also clarify the status of the defect effect for directed figures.


    Volume: Vol. 11 no. 2
    Section: Automata, Logic and Semantics
    Published on: January 1, 2009
    Imported on: March 26, 2015
    Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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