Multiparty Karchmer-Wigderson Games and Threshold Circuits

Alexander Kozachinskiy; Vladimir Podolskii

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arXiv · 2002.07444

Multiparty Karchmer-Wigderson Games and Threshold Circuits

Alexander Kozachinskiy·Vladimir Podolskii

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Abstract

We suggest a generalization of Karchmer-Wigderson communication games to the multiparty setting. Our generalization turns out to be tightly connected to circuits consisting of threshold gates. This allows us to obtain new explicit constructions of such circuits for several functions. In particular, we provide an explicit (polynomial-time computable) log-depth monotone formula for Majority function, consisting only of 3-bit majority gates and variables. This resolves a conjecture of Cohen et al. (CRYPTO 2013).

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BibTeX RIS

Alexander Kozachinskiy, Vladimir Podolskii. 2020-02-18. Multiparty Karchmer-Wigderson Games and Threshold Circuits. https://arxiv.org/abs/2002.07444

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