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arXiv · 1901.06900

MSO+nabla is undecidable

Mikołaj Bojańczyk·Edon Kelmendi·Michał Skrzypczak
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Abstract

This paper is about an extension of monadic second-order logic over the full binary tree, which has a quantifier saying ``almost surely a branch {\pi} \in {0, 1}^w satisfies a formula {\phi}({\pi})''. This logic was introduced by Michalewski and Mio; we call it MSO+nabla following notation of Shelah and Lehmann. The logic MSO+nabla subsumes many qualitative probabilistic formalisms, including qualitative probabilistic CTL, probabilistic LTL, or parity tree automata with probabilistic acceptance conditions. We show that it is undecidable to check if a given sentence of MSO+nabla is true in the full binary tree.

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Mikołaj Bojańczyk, Edon Kelmendi, Michał Skrzypczak. 2019-01-21. MSO+nabla is undecidable. https://arxiv.org/abs/1901.06900

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