We introduced the notation of a set of prohibitions and give definitions of a
complete set and a crucial word with respect to a given set of prohibitions. We
consider 3 particular sets which appear in different areas of mathematics and
for each of them examine the length of a crucial word. One of these sets is
proved to be incomplete. The problem of determining lengths of words that are
free from a set of prohibitions is shown to be NP-complete, although the
related problem of whether or not a given set of prohibitions is complete is
known to be effectively solvable.Comment: 16 page
