Transformations between Minimally f-free Words

A transformation between a pair of binary words u and v of the same length and Hamming distance d is a sequence of words w0=u, w1, w2, ... , wd=v, such that wi differs from w(i+1) only in one position. The transformation is said to be f-free, for a given word f, if f is absent in all wi, i.e. if f is not a factor of any wi. A word f is good if there exists an f-free transformation between any pair of f-free words of same length. Good words have been completely characterized using combinatorial methods on words. A word f is a minimal absent word for w if f is an absent word in w but all its proper factors occur in w. We consider f-free transformations between pairs of words u and v for which f is a minimal absent word and study how the property of including the proper factors of f can be maintained in the intermediate words of the transformation.