One of the basic tasks in compiler construction, document processing, hypertext software and similar projects is the efficient construction of a finite automaton from a given rational (regular) expression. The aim of the present paper is to give an exposition and a formal proof of the background for the algorithm of Berry and Sethi relating the computation involved to a well-known family of recognizable languages, the local languages.
Berstel, J., & Pin, J. E. (1996). Local languages and the Berry-Sethi algorithm. Theoretical Computer Science, 155(2), 439–446. https://doi.org/10.1016/0304-3975(95)00104-2