Lower bounds on balancing sets and depth-2 threshold circuits

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00507746" target="_blank" >RIV/67985840:_____/19:00507746 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2019.72" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ICALP.2019.72</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2019.72" target="_blank" >10.4230/LIPIcs.ICALP.2019.72</a>

Result language

angličtina

Original language name

Lower bounds on balancing sets and depth-2 threshold circuits

Original language description

There are various notions of balancing set families that appear in combinatorics and computer science. For example, a family of proper non-empty subsets S_1,...,S_k subset [n] is balancing if for every subset X subset {1,2,...,n} of size n/2, there is an i in [k] so that |S_i cap X| = |S_i|/2. We extend and simplify the framework developed by Hegedüs for proving lower bounds on the size of balancing set families. We prove that if n=2p for a prime p, then k >= p. For arbitrary values of n, we show that k >= n/2 - o(n). We then exploit the connection between balancing families and depth-2 threshold circuits. This connection helps resolve a question raised by Kulikov and Podolskii on the fan-in of depth-2 majority circuits computing the majority function on n bits. We show that any depth-2 threshold circuit that computes the majority on n bits has at least one gate with fan-in at least n/2 - o(n). We also prove a sharp lower bound on the fan-in of depth-2 threshold circuits computing a specific weighted threshold function.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2019

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

ISBN

978-3-95977-109-2

ISSN

1868-8969

e-ISSN

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Number of pages

14

Pages from-to

72

Publisher name

Schloss Dagstuhl, Leibniz-Zentrum für Informatik

Place of publication

Dagstuhl

Event location

Patras

Event date

Jul 8, 2019

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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