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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Bibliographic Details
Published in2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) pp. 1 - 13
Main Authors Niwinski, Damian, Parys, Pawel, Skrzypczak, Michal
Format Conference Proceeding
LanguageEnglish
Published IEEE 26.06.2023
Subjects
Automata
Computational logic
Computer science
Decision problems
Formal Languages
Probabilistic logic
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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.
DOI:10.1109/LICS56636.2023.10175800