Effect of quantified irreducibility on the computability of subshift entropy

TL;DR

This paper investigates the computational complexity of calculating topological entropy in subshifts with mixing restrictions, identifying the precise irreducibility threshold where the problem transitions from computable to uncomputable across various dimensions.

Contribution

It determines the exact irreducibility threshold for subshifts with decidable languages, extending previous results to a broader class and all dimensions.

Findings

Identified the irreducibility threshold for subshifts with decidable languages.

Extended the understanding of entropy computability to more general subshift classes.

Provided a comprehensive analysis applicable to multidimensional cases.

Abstract

We study the difficulty of computing topological entropy of subshifts subjected to mixing restrictions. This problem is well-studied for multidimensional subshifts of finite type : there exists a threshold in the irreducibility rate where the difficulty jumps from computable to uncomputable, but its location is an open problem. In this paper, we establish the location of this threshold for a more general class, subshifts with decidable languages, in any dimension.