OpenAI reports a uniform generalized star-height bound

Every regular language over a finite alphabet has a generalized regular expression over that same alphabet whose Kleene-star nesting height is at most thirteen, with complement taken relative to the same free monoid.

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Understanding the problem

Read the background

Every regular language over a finite alphabet has a generalized regular expression over that same alphabet whose Kleene-star nesting height is at most thirteen, with complement taken relative to the same free monoid.

Why it matters

If correct, establishes a universal finite bound on the generalized star height of regular languages.

What counts as progress

Is generalized star height uniformly bounded over every finite alphabet and regular language?

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