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, ...

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, ...

We give a complete proof of the following theorem: Every de Bruijn sequence of order n in at least three symbols can be extended to a de Bruijn sequence of order n+1. Every de Bruijn sequence of order n in two symbols can ...

We study a construction published by Donald Knuth in 1965 yielding a completely uniformly distributed sequence of real numbers. Knuth's work is based on de Bruijn sequences of increasing orders and alphabet sizes, which ...

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 ...

Let G = (V, A) be an Eulerian directed graph with an arc-labeling. In this work we study the problem of finding an Eulerian circuit of lexicographically minimal label among all Eulerian circuits of the graph. We prove that ...