Techniques for establishing star height of regular sets

Abstract

This paper deals with restricted star height of regular sets, as defined by L. C. Eggan. Theorems relating the star height of a regular event with the structure of the reduced deterministic automaton recognizing the event are presented. These theorems provide new techniques for establishing star height; in many cases the exact star height of the given regular set can be determined and in others lower bounds to the star height are found. Some results concerning the star height of sets recognized by reset-free state graphs (i.e., partial state graphs in which two transitions labelled by the same input letter never enter the same state) are also obtained, e.g., the star height of any event recognized by a group-free reset-free state graph equals the cycle rank of the state graph.