The Probabilistic Rabin Tree Theorem
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 additio...
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Published in | 2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) pp. 1 - 13 |
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Main Authors | , , |
Format | Conference Proceeding |
Language | English |
Published |
IEEE
26.06.2023
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Subjects | |
Online Access | Get full text |
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Summary: | 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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DOI: | 10.1109/LICS56636.2023.10175800 |