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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > MAJORITY FUNCTION:
Reports tagged with majority function:
TR20-017 | 18th February 2020
Alexander Kozachinskiy, Vladimir Podolskii

Multiparty Karchmer-Wigderson Games and Threshold Circuits

Revisions: 1

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 ... more >>>


TR22-030 | 18th February 2022
Aniruddha Biswas, Palash Sarkar

On The ''Majority is Least Stable'' Conjecture.

Revisions: 1

We show that the ''majority is least stable'' conjecture is true for $n=1$ and $3$ and false for all odd $n\geq 5$.

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TR23-153 | 19th October 2023
Natalia Dobrokhotova-Maikova, Alexander Kozachinskiy, Vladimir Podolskii

Towards Simpler Sorting Networks and Monotone Circuits for Majority

In this paper, we study the problem of computing the majority function by low-depth monotone circuits and a related problem of constructing low-depth sorting networks. We consider both the classical setting with elementary operations of arity $2$ and the generalized setting with operations of arity $k$, where $k$ is a ... more >>>


TR24-074 | 11th April 2024
Vaibhav Krishan, Sundar Vishwanathan

Towards ACC Lower Bounds using Torus Polynomials

The class $ACC$ consists of Boolean functions that can be computed by constant-depth circuits of polynomial size with $AND, NOT$ and $MOD_m$ gates, where $m$ is a natural number. At the frontier of our understanding lies a widely believed conjecture asserting that $MAJORITY$ does not belong to $ACC$. The Boolean ... more >>>




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