Overlap-free words and finite automata

AbstractA method to represent certain words on a binary alphabet by shorter words on a larger alphabet is introduced. We prove that overlap-free words are represented by the words of a rational language. Several consequences are derived concerning the density function of the set of overlap-free words on a binary alphabet and the prolongability of overlap-free words. In particular, efficient algorithms are obtained computing the density function of the set of overlap-free words on a binary alphabet, testing whether a word on a binary alphabet is overlap-free and computing its depth