Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2021

The relationship between word complexity and computational complexity in subshifts

Résumé

We prove several results about the relationship between the word complexity function of a subshift and the set of Turing degrees of points of the subshift, which we call the Turing spectrum. Among other results, we show that a Turing spectrum can be realized via a subshift of linear complexity if and only if it consists of the union of a finite set and a finite number of cones, that a Turing spectrum can be realized via a subshift of exponential complexity (i.e. positive entropy) if and only if it contains a cone, and that every Turing spectrum which either contains degree 0 or is a union of cones is realizable by subshifts with a wide range of 'intermediate' complexity growth rates between linear and exponential.

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hal-02063174 , version 1 (10-03-2019)

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Ronnie Pavlov, Pascal Vanier. The relationship between word complexity and computational complexity in subshifts. Discrete and Continuous Dynamical Systems - Series A, 2021, 41 (4), pp.1627-1648. ⟨10.3934/dcds.2020334⟩. ⟨hal-02063174⟩
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