An answer to a question about finite maximal prefix sets of words

Abstract

M.P. Schützenberger has proved that two finite sets of words are maximal prefix if their product is unambiguous and maximal prefix [3]. In [1], the authors ask whether the unambiguity hypothesis is necessary. We answer this question positively by giving an example of a finite maximal prefix and ambiguous product of which the two factors are not maximal prefix.