We give an alternative proof for the existing result that recurrent graph neural networks working with reals have the same expressive power in restriction to monadic second-order logic MSO as the graded modal substitution calculus. The proof is based on constructing distributed automata that capture all MSO-definable node properties over trees. We also consider some variants of the acceptance conditions.
@article{arxiv.2505.07816,
title = {Graph neural networks and MSO},
author = {Veeti Ahvonen and Damian Heiman and Antti Kuusisto},
journal= {arXiv preprint arXiv:2505.07816},
year = {2025}
}