On the relative power of reduction notions in arithmetic circuit complexity

Christian Ikenmeyer; Stefan Mengel

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arXiv · 1609.05942

On the relative power of reduction notions in arithmetic circuit complexity

Christian Ikenmeyer·Stefan Mengel

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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.

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Christian Ikenmeyer, Stefan Mengel. 2016-09-19. On the relative power of reduction notions in arithmetic circuit complexity. https://arxiv.org/abs/1609.05942

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