## Regular languages of star height one.(English)Zbl 0547.68072

The paper studies the old and so far open problem of determining the star height of a given regular language. The author shows that for any regular language R, there exists a regular expression E in string form such that (1) E denotes R, (2) the star height of E is equal to that of R, and (3) for any word w which appears in E, $$l(w)\leq 16m(m+2)(h(R)m(m+2)+1),$$ where l(w) is the length of w, h(R) is the star height of R, and m is the number of elements of the syntactic semigroup of R. This result together with a theorem in the paper ”Representation theorems on regular languages” by K. Hashiguchi [J. Comput. Syst. Sci. 27, 101-115 (1983; Zbl 0516.68063)] provides an algorithm for deciding whether a given regular language is of star height one.
Reviewer: M.Linna

### MSC:

 68Q45 Formal languages and automata

### Keywords:

star height; regular language

Zbl 0516.68063
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