Abstract
We employ a two-dimensional automaton defined in [5] to recognize a class of two-dimensional shifts of finite type having the property that every admissable block found within the related local picture language can be extended to a point of the subshift. Here, we show that the automaton accurately represents the image of the represented two-dimensional shift of finite type under a block code. We further show that such automata can be used to check for a certain type of two-dimensional transitivity in the factor language of the corresponding shift space and how this relates to periodicity in the two-dimensional case. The paper closes with a notion of “follower sets” used to reduce the size of the automata representing two-dimensional sofic shifts.
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Jonoska, N., Pirnot, J.B. (2007). Finite State Automata Representing Two-Dimensional Subshifts. In: Holub, J., Žďárek, J. (eds) Implementation and Application of Automata. CIAA 2007. Lecture Notes in Computer Science, vol 4783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76336-9_26
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DOI: https://doi.org/10.1007/978-3-540-76336-9_26
Publisher Name: Springer, Berlin, Heidelberg
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