Handbook of theoretical computer science (vol. B)
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In "On regularity of context-free languages" [Theoret. Comput. Sci. 27 (1983) 311], Ehrenfeucht et al. showed that a set L of finite words is regular if and only if L is ≤-closed under some monotone well-quasi-order (WQO) ≤ over finite words. We extend this result to regular ω-languages. That is, (1) an ω-language L is regular if and only if L is ≤-closed under a periodic extension ≤ of some monotone WQO over finite words, and (2) an ω-language L is regular if and only if L is ≤-closed under a WQO ≤ over ω-words that is a continuous extension of some monotone WQO over finite words.