Computing majority with low-fan-in majority queries

11/28/2017
by   Gleb Posobin, et al.
0

In this paper we examine the problem of computing majority function MAJ_n on n bits by depth-two formula, where each gate is a majority function on at most k inputs. We present such formula that gives the first nontrivial upper bound for this problem, with k = 2/3 n + 4. This answers an open question in [Kulikov, Podolskii, 2017]. We also look at this problem in adaptive setting - when we are allowed to query for value of MAJ_k on any subset, and wish to minimize the number of such queries. We give a simple lower bound for this setting with n/k queries, and we present two algorithms for this model: the first one makes ≈ 2n/k k queries in the case when we are limited to the standard majority functions, and the second one makes n/k k queries when we are allowed to change the threshold of majority function.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/07/2019

Testing convexity of functions over finite domains

We establish new upper and lower bounds on the number of queries require...
research
12/02/2021

Generalized Framework for Group Testing: Queries, Feedbacks and Adversaries

In the Group Testing problem, the objective is to learn a subset K of so...
research
01/21/2018

The Optimal Majority Threshold as a Function of the Variation Coefficient of the Environment

Within the model of social dynamics determined by collective decisions i...
research
01/28/2022

The Price of Majority Support

We consider the problem of finding a compromise between the opinions of ...
research
08/10/2018

The effective entropy of next/previous larger/smaller value queries

We study the problem of storing the minimum number of bits required to a...
research
02/06/2013

Learning Bayesian Nets that Perform Well

A Bayesian net (BN) is more than a succinct way to encode a probabilisti...
research
09/07/2023

Noisy Computing of the 𝖮𝖱 and 𝖬𝖠𝖷 Functions

We consider the problem of computing a function of n variables using noi...

Please sign up or login with your details

Forgot password? Click here to reset