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arXiv · 2304.12158

On the Computability of Measures of Regular Sets of Infinite Trees

Damian Niwiński·Paweł Parys·Michał Skrzypczak
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Abstract

The Rabin tree theorem yields an algorithm to solve the satisfiability problem for monadic second-order logic over infinite trees. Here we solve the probabilistic variant of this problem. Namely, we show how to compute the probability that a randomly chosen tree satisfies a given formula. We additionally show that this probability is an algebraic number. This closes a line of research where similar results were shown for formalisms weaker than the full monadic second-order logic.

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Damian Niwiński, Paweł Parys, Michał Skrzypczak. 2023-04-24. On the Computability of Measures of Regular Sets of Infinite Trees. https://arxiv.org/abs/2304.12158

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