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- W2965659827 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 $pi in{0,1}^{omega}$ satisfies a formula $varphi(pi)$ ”, This logic was introduced by Michalewski and Mio; we call it $mathrm{MSO}+nabla$ following notation of Shelah and Lehmann. The logic $mathrm{Mso}+nabla$ subsumes many qualitative probabilistic formalisms, including qualitative probabilistic $check$ , probabilistic LTL, or parity tree automata with probabilistic acceptance conditions. We show that it is undecidable to check if a given sentence of $mathrm{MSO}+nabla$ is true in the full binary tree11Independently and in parallel another proof of this result was given employing different techniques in [3].." @default.
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- W2965659827 date "2019-06-01" @default.
- W2965659827 modified "2023-09-25" @default.
- W2965659827 title "MSO+∇ is undecidable" @default.
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- W2965659827 doi "https://doi.org/10.1109/lics.2019.8785892" @default.
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