  We present a new approach to edit distance attacks on certain
clock-controlled generators, which applies basic concepts of Graph Theory to
simplify the search trees of the original attacks in such a way that only the
most promising branches are analyzed. In particular, the proposed improvement
is based on cut sets defined on some graphs so that certain shortest paths
provide the edit distances. The strongest aspects of the proposal are that the
obtained results from the attack are absolutely deterministic, and that many
inconsistent initial states of the target registers are recognized beforehand
and avoided during search.
