A Sufficient Condition for Hanna Neumann Property of Submonoids of a Free Monoid

TL;DR

This paper extends automata-theoretic methods to establish a sufficient condition for the Hanna Neumann property in all finitely generated submonoids of a free monoid generated by finite prefix sets, including a new rank formula.

Contribution

It provides a general sufficient condition for the Hanna Neumann property for submonoids generated by finite prefix sets, broadening previous specific cases.

Findings

Established a sufficient condition for the Hanna Neumann property.

Derived a general rank formula for submonoids accepted by semi-flower automata.

Extended previous results to a wider class of submonoids.

Abstract

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.