Extensions of ω-Regular Languages

02/21/2020

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by   Mikołaj Bojańczyk, et al.

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We consider extensions of monadic second order logic over ω-words, which are obtained by adding one language that is not ω-regular. We show that if the added language L has a neutral letter, then the resulting logic is necessarily undecidable. A corollary is that the ω-regular languages are the only decidable Boolean-closed full trio over ω-words.