Rationality and computability of the covering radius for sofic shifts

2026-03-22

AI Summary

This study investigates the covering radius of sofic shift systems, a quantity of fundamental importance in information transmission over noisy channels. By leveraging the labeled graph representation of sofic shifts and integrating tools from symbolic dynamics and graph algorithms, the authors establish for the first time that the covering radius of any sofic shift is necessarily a rational number. Furthermore, they propose an explicit algorithm that effectively computes this value directly from the underlying graph structure. This work not only confirms the rationality of the covering radius but also demonstrates its computability, thereby providing both a theoretical foundation and a practical computational tool for applications in coding theory and information theory.

Technology Category

Knowledge Representation and Reasoning: Computational Complexity of ReasoningPlanning, Routing, and Scheduling: Optimization of Spatio-temporal SystemsMachine Learning: Probabilistic Circuits and Graphical Models

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSecurity and Privacy: Large-scale security measurementsSystems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

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.

Problem

• covering radius
• sofic shifts
• rationality
• computability
• shift spaces

Innovation

• covering radius
• sofic shifts
• rationality
• computability
• labeled graph