The concept of star height of regular expressions, introduced by L. C. Eggan in 1963, is not usually discussed in textbooks on theoretical science. The concept is relatively simple, and its meaning can be seen in these examples: star height h ( a ) = 0; h ( a * b ) = 1; h ( ( a + b* ) * b ) = 2. Many authors have attempted to develop algorithms for finding the star height of regular sets.

This paper is a continuation of the author’s long 1988 paper, in which he introduced a concept of relative star height and presented an algorithm for determining it [1]. In this paper, he introduces the concept of relative inclusion star height and develops relevant algorithms.