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arXiv · 2002.09393

Extensions of $ω$-Regular Languages

Mikołaj Bojańczyk·Edon Kelmendi·Rafał Stefański·Georg Zetzsche
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Abstract

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.

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Mikołaj Bojańczyk, Edon Kelmendi, Rafał Stefański, Georg Zetzsche. 2020-02-21. Extensions of $ω$-Regular Languages. https://arxiv.org/abs/2002.09393

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