Rationality and computability of the covering radius for sofic shifts

TL;DR

This paper proves that the covering radius of a primitive sofic shift is always rational and provides an algorithm to compute it from a labeled graph, aiding information theory applications.

Contribution

It establishes the rationality of the covering radius for primitive sofic shifts and introduces a method to compute it from graph representations.

Findings

Covering radius of primitive sofic shifts is rational.

An algorithm for computing the covering radius from labeled graphs is provided.

The results facilitate applications in data transmission over noisy channels.

Abstract

The covering radius of a shift space is a quantity of interest for information-theoretic applications of data transmission over noisy channels. We prove that the covering radius of a primitive sofic shift is a rational number, and describe an algorithm to compute the covering radius from a labeled graph presentation.