Optimal composition theorem for randomized query complexity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00581950" target="_blank" >RIV/67985840:_____/23:00581950 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4086/toc.2021.v017a008" target="_blank" >http://dx.doi.org/10.4086/toc.2021.v017a008</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4086/toc.2023.v019.a009" target="_blank" >10.4086/toc.2023.v019.a009</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimal composition theorem for randomized query complexity

Popis výsledku v původním jazyce

For any set S, any relation F subset of {0, 1}(n) x S and any partial Boolean function, defined on a subset of {0, 1}(m), we show that R-1/3 (f o g(n)) is an element of Omega (R-4/9(f) center dot root R-1/3(g)), where R-epsilon(center dot) stands for the bounded-error randomized query complexity with error at most epsilon, and f o g(n) subset of ({0, 1}(m))(n) x S denotes the composition of 5 with = instances of g. This result is new even in the special case when S = {0, 1} and g is a total function. We show that the new composition theorem is optimal for the general case of relations: A relation f(0) and a partial Boolean function g(0) are constructed, such that R-4/9 (f(0)) is an element of Theta(root n), R-1/3(g(0)) is an element of Theta (n) and R-1/3(f(0) o g(0)(n)) is an element of Theta (n).nThe theorem is proved via introducing a new complexity measure, max-conflict complexity, denoted by chi(center dot). Its investigation shows that (chi) over bar (g) is an element of Omega(R-1/3(g)) for any partial Boolean function g and (R-1/3(f o g(n)) is an element of Omega(R-4/9(f) center dot (chi) over bar (g)) for any relation f, which readily implies the composition statement. It is further shown that (chi) over bar (g) is always at least as large as the sabotage complexity of g (introduced by Ben-David and Kothari in 2016).

Název v anglickém jazyce

Optimal composition theorem for randomized query complexity

Popis výsledku anglicky

For any set S, any relation F subset of {0, 1}(n) x S and any partial Boolean function, defined on a subset of {0, 1}(m), we show that R-1/3 (f o g(n)) is an element of Omega (R-4/9(f) center dot root R-1/3(g)), where R-epsilon(center dot) stands for the bounded-error randomized query complexity with error at most epsilon, and f o g(n) subset of ({0, 1}(m))(n) x S denotes the composition of 5 with = instances of g. This result is new even in the special case when S = {0, 1} and g is a total function. We show that the new composition theorem is optimal for the general case of relations: A relation f(0) and a partial Boolean function g(0) are constructed, such that R-4/9 (f(0)) is an element of Theta(root n), R-1/3(g(0)) is an element of Theta (n) and R-1/3(f(0) o g(0)(n)) is an element of Theta (n).nThe theorem is proved via introducing a new complexity measure, max-conflict complexity, denoted by chi(center dot). Its investigation shows that (chi) over bar (g) is an element of Omega(R-1/3(g)) for any partial Boolean function g and (R-1/3(f o g(n)) is an element of Omega(R-4/9(f) center dot (chi) over bar (g)) for any relation f, which readily implies the composition statement. It is further shown that (chi) over bar (g) is always at least as large as the sabotage complexity of g (introduced by Ben-David and Kothari in 2016).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GX19-27871X" target="_blank" >GX19-27871X: Efektivní aproximační algoritmy a obvodová složitost</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Theory of Computing

ISSN

1557-2862

e-ISSN

1557-2862

Svazek periodika

19

Číslo periodika v rámci svazku

December

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

35

Strana od-do

9

Kód UT WoS článku

001137473500001

EID výsledku v databázi Scopus

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