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On the relative power of reduction notions in arithmetic circuit complexity (1609.05942v1)
Published 19 Sep 2016 in cs.CC
Abstract: We show that the two main reduction notions in arithmetic circuit complexity, p-projections and c-reductions, differ in power. We do so by showing unconditionally that there are polynomials that are VNP-complete under c-reductions but not under p-projections. We also show that the question of which polynomials are VNP-complete under which type of reductions depends on the underlying field.