  In this paper we present a procedure for computing the rational sum of the
Hilbert series of a finitely generated monomial right module $N$ over the free
associative algebra $K\langle x_1,\ldots,x_n \rangle$. We show that such
procedure terminates, that is, the rational sum exists, when all the cyclic
submodules decomposing $N$ are annihilated by monomial right ideals whose
monomials define regular formal languages. The method is based on the iterative
application of the colon right ideal operation to monomial ideals which are
given by an eventual infinite basis. By using automata theory, we prove that
the number of these iterations is a minimal one. In fact, we have experimented
efficient computations with an implementation of the procedure in Maple which
is the first general one for noncommutative Hilbert series.
