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Preprint in the OpenAI Math release

Generalized Star Height at Most Three

OpenAI

Abstract

Every regular language over a finite alphabet has generalized star height at most three, with complement taken in the same free monoid. We express finite-monoid computations using a prefix code of word pieces.

open until 1 Jan 2028

est. 50% chance this result is independently verified by the end of 2027.

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