The relationship between word complexity and computational complexity in subshifts
Discrete Mathematics
2019-03-12 v1 Computational Complexity
Formal Languages and Automata Theory
Dynamical Systems
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.
Cite
@article{arxiv.1903.04325,
title = {The relationship between word complexity and computational complexity in subshifts},
author = {Ronnie Pavlov and Pascal Vanier},
journal= {arXiv preprint arXiv:1903.04325},
year = {2019}
}