A composition theorem for randomized query complexity via Max-conflict complexity

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00507748" target="_blank" >RIV/67985840:_____/19:00507748 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2019.64" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ICALP.2019.64</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2019.64" target="_blank" >10.4230/LIPIcs.ICALP.2019.64</a>

Result language

angličtina

Original language name

A composition theorem for randomized query complexity via Max-conflict complexity

Original language description

For any relation f subseteq {0,1}^n x S and any partial Boolean function g:{0,1}^m -> {0,1,*}, we show that R_{1/3}(f o g^n) in Omega(R_{4/9}(f) * sqrt{R_{1/3}(g)}) , where R_epsilon(*) stands for the bounded-error randomized query complexity with error at most epsilon, and f o g^n subseteq ({0,1}^m)^n x S denotes the composition of f with n instances of g. The new composition theorem is optimal, at least, for the general case of relational problems: A relation f_0 and a partial Boolean function g_0 are constructed, such that R_{4/9}(f_0) in Theta(sqrt n), R_{1/3}(g_0)in Theta(n) and R_{1/3}(f_0 o g_0^n) in Theta(n). The theorem is proved via introducing a new complexity measure, max-conflict complexity, denoted by bar{chi}(*). Its investigation shows that bar{chi}(g) in Omega(sqrt{R_{1/3}(g)}) for any partial Boolean function g and R_{1/3}(f o g^n) in Omega(R_{4/9}(f) * bar{chi}(g)) for any relation f, which readily implies the composition statement. It is further shown that bar{chi}(g) is always at least as large as the sabotage complexity of g.

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

13

Pages from-to

64

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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