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Weighted Gate Elimination: Boolean Dispersers for Quadratic Varieties Imply Improved Circuit Lower Bounds

Authors:

Alexander Golovnev,

Alexander S. KulikovAuthors Info & Claims

ITCS '16: Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science

Pages 405 - 411

https://doi.org/10.1145/2840728.2840755

Published: 14 January 2016 Publication History

Abstract

In this paper we motivate the study of Boolean dispersers for quadratic varieties by showing that an explicit construction of such objects gives improved circuit lower bounds. An (n,k,s)-quadratic disperser is a function on n variables that is not constant on any subset of Fn/2 of size at least s that can be defined as the set of common roots of at most k quadratic polynomials. We show that if a Boolean function f is a (n, 1.83n, 2^g(n)-quadratic disperser for any function g(n)=o(n) then the circuit size of f is at least 3.11n. In order to prove this, we generalize the gate elimination method so that the induction works on the size of the variety rather than on the number of variables as in previously known proofs.

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Cited By

Li JYang TLeonardi SGupta A(2022)3.1n − o(n) circuit lower bounds for explicit functionsProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3519976(1180-1193)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3519976
Find MGolovnev AHirsch EKulikov A(2016)A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2016.19(89-98)Online publication date: Oct-2016
https://doi.org/10.1109/FOCS.2016.19

Index Terms

Weighted Gate Elimination: Boolean Dispersers for Quadratic Varieties Imply Improved Circuit Lower Bounds
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

ITCS '16: Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science

January 2016

422 pages

ISBN:9781450340571

DOI:10.1145/2840728

Program Chair:
Madhu Sudan
Harvard University

Copyright © 2016 ACM.

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Published: 14 January 2016

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Government of the Russian Federation
National Science Foundation

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ITCS'16

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SIGACT

ITCS'16: Innovations in Theoretical Computer Science

January 14 - 17, 2016

Massachusetts, Cambridge, USA

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ITCS '16 Paper Acceptance Rate 40 of 145 submissions, 28%;

Overall Acceptance Rate 172 of 513 submissions, 34%

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Cited By

Li JYang TLeonardi SGupta A(2022)3.1n − o(n) circuit lower bounds for explicit functionsProceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3519935.3519976(1180-1193)Online publication date: 9-Jun-2022
https://dl.acm.org/doi/10.1145/3519935.3519976
Find MGolovnev AHirsch EKulikov A(2016)A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2016.19(89-98)Online publication date: Oct-2016
https://doi.org/10.1109/FOCS.2016.19

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