  Using automata-theoretic approach, Giambruno and Restivo have investigated on
the intersection of two finitely generated submonoids of the free monoid over a
finite alphabet. In particular, they have obtained Hanna Neumann property for a
special class of submonoids generated by finite prefix sets. This work
continues their work and provides a sufficient condition for Hanna Neumann
property for the entire class of submonoids generated by finite prefix sets. In
this connection, a general rank formula for the submonoids which are accepted
by semi-flower automata is also obtained.

Formal Languages and Automata Theory