Symmetric MOD_m circuits require subexponential size to compute n-ary AND, with the bound matched by known depth-2 constructions.
‘Symmetric Algebraic Circuits and Homo- morphism Polynomials’
2 Pith papers cite this work. Polarity classification is still indexing.
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Separating modules of support-degree k equate to O(k)-subgraph counts, those of symmetric circuit size n^Θ(k) equate to Θ(k)-WL, and their multiplicities equate to differing automorphism cycle indices.
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Optimal Lower Bounds for Symmetric Modular Circuits
Symmetric MOD_m circuits require subexponential size to compute n-ary AND, with the bound matched by known depth-2 constructions.
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Graph Isomorphism and Representation Theory
Separating modules of support-degree k equate to O(k)-subgraph counts, those of symmetric circuit size n^Θ(k) equate to Θ(k)-WL, and their multiplicities equate to differing automorphism cycle indices.