New lower bounds against homogeneous non-commutative circuits

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00575139" target="_blank" >RIV/67985840:_____/23:00575139 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2023.13" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.CCC.2023.13</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2023.13" target="_blank" >10.4230/LIPIcs.CCC.2023.13</a>

Result language

angličtina

Original language name

New lower bounds against homogeneous non-commutative circuits

Original language description

We give several new lower bounds on size of homogeneous non-commutative circuits. We present an explicit homogeneous bivariate polynomial of degree d which requires homogeneous non-commutative circuit of size Ω(d/log d). For an n-variate polynomial with n > 1, the result can be improved to Ω(nd), if d ≤ n, or Ω(ndloglognd), if d ≥ n. Under the same assumptions, we also give a quadratic lower bound for the ordered version of the central symmetric polynomial.

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

2023

Confidentiality

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

Article name in the collection

38th Computational Complexity Conference (CCC 2023)

ISBN

978-3-95977-282-2

ISSN

1868-8969

e-ISSN

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Number of pages

10

Pages from-to

13

Publisher name

Schloss Dagstuhl, Leibniz-Zentrum für Informatik

Place of publication

Dagstuhl

Event location

Warwick

Event date

Jul 17, 2023

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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