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Extensions of ω-regular Languages

Edon Kelmendi ( University of Oxford )
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 cone over ω-words.

Joint work with: Mikołaj Bojańczyk, Rafał Stefański and Georg Zetzsche.

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