Minimum de Bruijn Sequence in a Language with Forbidden Substrings

TL;DR

This paper investigates conditions under which a greedy traversal strategy on de Bruijn graphs yields minimal de Bruijn sequences for languages with forbidden substrings.

Contribution

It characterizes languages for which the minimal de Bruijn sequence can be obtained via a greedy minimum-label arc traversal strategy.

Findings

Identifies classes of languages where the strategy produces Eulerian cycles.

Provides conditions ensuring the minimal de Bruijn sequence is obtained.

Analyzes the structure of de Bruijn graphs with forbidden substrings.

Abstract

Let be the following strategy to construct a walk in a labeled digraph: at each vertex, we follow the unvisited arc of minimum label. In this work we study for which languages, applying the previous strategy over the corresponding de Bruijn graph, we finish with an Eulerian cycle, in order to obtain the minimal de Bruijn sequence of the language.