On the monotone complexity of the shift operator

Igor S. Sergeev

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arXiv · 1905.10747

On the monotone complexity of the shift operator

Igor S. Sergeev

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Abstract

We show that the complexity of minimal monotone circuits implementing a monotone version of the permutation operator on $n$ boolean vectors of length $q$ is $\Theta(qn\log n)$. In particular, we obtain an alternative way to prove the known complexity bound $\Theta(n\log n)$ for the monotone shift operator on $n$ boolean inputs.

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Igor S. Sergeev. 2019-05-26. On the monotone complexity of the shift operator. https://arxiv.org/abs/1905.10747

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