A sufficient condition for the Hanna Neumann property of submonoids of a free monoid

Using an automata-theoretic approach, Giambruno and Restivo have investigated the intersection of two finitely generated submonoids of the free monoid over a finite alphabet. In particular, they have obtained the 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 the 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.