P_C ≠ NP_C in the BSS model over C implies VP^0 ≠ VNP^0 in the constant-free Valiant classes over C, with an analogous nonuniform statement.
On the complexity of numerical analysis.SIAM J
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Intractability of Hilbert's Nullstellensatz implies algebraic hardness of permanent
P_C ≠ NP_C in the BSS model over C implies VP^0 ≠ VNP^0 in the constant-free Valiant classes over C, with an analogous nonuniform statement.