  The word position automaton was introduced by Glushkov and McNaughton in the
early 1960. This automaton is homogeneous and has (||\E||+1) states for a word
expression of alphabetic width ||\E||. This kind of automata is extended to
regular tree expressions.
  In this paper, we give an efficient algorithm that computes the \Follow sets,
which are used in different algorithms of conversion of a regular expression
into tree automata. In the following, we consider the k-position tree automaton
construction. We prove that for a regular expression \E of a size |\E| and
alphabetic width ||\E||, the \Follow sets can be computed in O(||\E||\cdot
|\E|) time complexity.
