The Boolean Power of ReLU

We prove that, on finite simple undirected graphs equipped with a single Boolean node feature, the Boolean queries expressible in Sigma-MPLang, for any collection Sigma of eventually constant activation functions and with arbitrary real coefficients, form a strict subclass of the Boolean queries expressible in ReLU-MPLang. We thereby settle a recently posed open problem: whether ReLU-MPLang is more powerful than trReLU-MPLang when it comes to Boolean queries. In particular, this implies that ReLU-GNNs are strictly more expressive than TrReLU,id-GNNs with respect to Boolean queries on Boolean-featured graphs.