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arXiv · 1901.04349

Monadic Second-Order Logic with Path-Measure Quantifier is Undecidable

Raphaël Berthon·Emmanuel Filiot·Shibashis Guha·Bastien Maubert·Aniello Murano·Laureline Pinault·Jean-François Raskin·Sasha Rubin
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Abstract

We prove that the theory of Monadic Second-Order logic (MSO) of the infinite binary tree extended with qualitative path-measure quantifier is undecidable. This quantifier says that the set of infinite paths in the tree that satisfies some formula has Lebesgue-measure one. To do this we prove that the emptiness problem of qualitative universal parity tree automata is undecidable. Qualitative means that a run of a tree automaton is accepting if the set of paths in the run that satisfy the acceptance condition has Lebesgue-measure one.

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Raphaël Berthon, Emmanuel Filiot, Shibashis Guha, Bastien Maubert, Aniello Murano, Laureline Pinault, Jean-François Raskin, Sasha Rubin. 2019-01-14. Monadic Second-Order Logic with Path-Measure Quantifier is Undecidable. https://arxiv.org/abs/1901.04349

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