English

On the Computability of Measures of Regular Sets of Infinite Trees

Logic in Computer Science 2024-11-22 v2

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.

Keywords

Cite

@article{arxiv.2304.12158,
  title  = {On the Computability of Measures of Regular Sets of Infinite Trees},
  author = {Damian Niwiński and Paweł Parys and Michał Skrzypczak},
  journal= {arXiv preprint arXiv:2304.12158},
  year   = {2024}
}