Random walks on semaphore codes and delay de Bruijn semigroups

TL;DR

This paper introduces a novel approach to analyzing random walks on de Bruijn graphs using right congruences and semaphore codes, simplifying the computation of hitting times and providing approximation methods.

Contribution

It presents a new framework connecting right congruences, semaphore codes, and random walks on de Bruijn graphs, enhancing computational techniques.

Findings

New method for computing hitting times in de Bruijn graphs

Introduction of special right congruences related to semaphore codes

Approximation techniques for general right congruences

Abstract

We develop a new approach to random walks on de Bruijn graphs over the alphabet $A$ through right congruences on $A^k$, defined using the natural right action of $A^+$. A major role is played by special right congruences, which correspond to semaphore codes and allow an easier computation of the hitting time. We show how right congruences can be approximated by special right congruences.