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Decidability of Irreducible Tree Shifts of Finite Type

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We reveal an algorithm for determining the complete prefix code irreducibility (CPC-irreducibility) of dyadic trees labeled by a finite alphabet. By introducing an extended directed graph representation of tree shift… Click to show full abstract

We reveal an algorithm for determining the complete prefix code irreducibility (CPC-irreducibility) of dyadic trees labeled by a finite alphabet. By introducing an extended directed graph representation of tree shift of finite type (TSFT), we show that the CPC-irreducibility of TSFTs is related to the connectivity of its graph representation, which is a similar result to one-dimensional shifts of finite type.

Keywords: finite type; irreducible tree; shifts finite; decidability irreducible; tree shifts; irreducibility

Journal Title: Journal of Statistical Physics
Year Published: 2019

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