Star Height Problem
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The star height problem in formal language theory is the question whether all regular languages can be expressed using regular expressions of limited star height, i.e. with a limited nesting depth of Kleene stars. Specifically, is a nesting depth of more than 2 required? If so, is there an algorithm to determine how many are required? The first question was answered in the negative when in 1963, Eggan gave examples of regular languages of star height n for every n.…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The star height problem in formal language theory is the question whether all regular languages can be expressed using regular expressions of limited star height, i.e. with a limited nesting depth of Kleene stars. Specifically, is a nesting depth of more than 2 required? If so, is there an algorithm to determine how many are required? The first question was answered in the negative when in 1963, Eggan gave examples of regular languages of star height n for every n. However, Eggan''s examples use a large alphabet, of size 2n-1 for the language with star height n. He thus asked whether we can also find examples over binary alphabets. This was proved to be true shortly afterwards by Dejean and Schützenberger (1966).