De Bruijn sequences and De Bruijn graphs for a general language
A de Bruijn sequence over a finite alphabet of span n is a cyclic string such that all words of length n appear exactly once as factors of this sequence. We extend this definition to a subset of words of length n, characterizing for which subsets exists a de Bruijn sequence. We also study some symbolic dynamical properties of these subsets extending the definition to a language defined by forbidden factors. For these kinds of languages we present an algorithm to produce a de Bruijn sequence. In this work we use graph-theoretic and combinatorial concepts to prove these results. (c) 2005 Elsevier B.V. All rights reserved.
de bruijn sequences de bruijn graphs eulerian labeled graphs combinatorics on words graph algorithms combinatorial problems