Computing k-th lyndon word and decoding lexicographically minimal de bruijn sequence

Abstract

Let ∑ be a finite ordered alphabet. We present polynomial-time algorithms for computing the k-th in the lexicographic order Lyndon word of a given length n over ∑ and counting Lyndon words of length n that are smaller than a given word. We also use the connections between Lyndon words and minimal de Bruijn sequences (theorem of Fredricksen and Maiorana) to develop the first polynomial time algorithm for decoding minimal de Bruijn sequence of any rank n (it determines the position of an arbitrary word of length n within the de Bruijn sequence). Our tools mostly rely on combinatorics on words and automata theory. © 2014 Springer International Publishing Switzerland.