DHNs with max/sum/mean aggregations correspond to UNFO and extensions with counting quantifiers, enabling decidability analysis for emptiness and subsumption problems.
Formally, for all1≤i≤m : if ind(v(i) 1 )≤2 ℓ or ind(v(i) 1 )≥2 n+1 −2ℓ+4 or ind(v(i) 2 )≤2 ℓ or ind(v(i) 2 )≥2 n+1 −2ℓ+4, thenind(v (i) 1 ) = ind(v(i) 2 )
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Expressive Power of Deep Homomorphism Networks over Relational Databases
DHNs with max/sum/mean aggregations correspond to UNFO and extensions with counting quantifiers, enabling decidability analysis for emptiness and subsumption problems.