  This paper situates itself in the theory of variable length codes and of
finite automata where the concepts of completeness and synchronization play a
central role. In this theoretical setting, we investigate the problem of
finding upper bounds to the minimal length of synchronizing words and
incompletable words of a finite language X in terms of the length of the words
of X. This problem is related to two well-known conjectures formulated by Cerny
and Restivo, respectively. In particular, if Restivo's conjecture is true, our
main result provides a quadratic bound for the minimal length of a
synchronizing pair of any finite synchronizing complete code with respect to
the maximal length of its words.
