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The relationship between word complexity and computational complexity in subshifts

Abstract : 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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https://hal.archives-ouvertes.fr/hal-02063174
Contributor : Pascal Vanier <>
Submitted on : Sunday, March 10, 2019 - 11:06:46 PM
Last modification on : Friday, October 4, 2019 - 1:12:43 AM
Document(s) archivé(s) le : Tuesday, June 11, 2019 - 2:31:13 PM

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  • HAL Id : hal-02063174, version 1
  • ARXIV : 1903.04325

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Ronnie Pavlov, Pascal Vanier. The relationship between word complexity and computational complexity in subshifts. 2019. ⟨hal-02063174⟩

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