When Six Gates are Not Enough

Michael Codish; Luís Cruz-Filipe; Michael Frank; Peter Schneider-Kamp

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arXiv · 1508.05737

When Six Gates are Not Enough

Michael Codish·Luís Cruz-Filipe·Michael Frank·Peter Schneider-Kamp

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Abstract

We apply the pigeonhole principle to show that there must exist Boolean functions on 7 inputs with a multiplicative complexity of at least 7, i.e., that cannot be computed with only 6 multiplications in the Galois field with two elements.

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Michael Codish, Luís Cruz-Filipe, Michael Frank, Peter Schneider-Kamp. 2015-08-24. When Six Gates are Not Enough. https://arxiv.org/abs/1508.05737

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