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Infinite Two-Dimensional Strong Prefix Codes: Characterization and Properties

Abstract : A two-dimensional code is defined as a set of rectangular pictures over an alphabet $\varSigma $ such that any picture over $\varSigma $ is tilable in at most one way with pictures in X. It is in general undecidable whether a set of pictures is a code, even in the finite case. Recently, finite strong prefix codes were introduced in [3] as a family of decidable picture codes. In this paper we study infinite strong prefix codes and give a characterization for the maximal ones based on iterated extensions. Moreover, we prove some properties regarding the measure of these codes.
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Marcella Anselmo, Dora Giammarresi, Maria Madonia. Infinite Two-Dimensional Strong Prefix Codes: Characterization and Properties. 23th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA), Jun 2017, Milan, Italy. pp.19-31, ⟨10.1007/978-3-319-58631-1_2⟩. ⟨hal-01656353⟩

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