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Optimal composition theorem for randomized query complexity

The result's identifiers

  • Result code in 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>

  • Result on the web

    <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>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Optimal composition theorem for randomized query complexity

  • Original language description

    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).

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

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

Result continuities

  • 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

Others

  • Publication year

    2023

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Theory of Computing

  • ISSN

    1557-2862

  • e-ISSN

    1557-2862

  • Volume of the periodical

    19

  • Issue of the periodical within the volume

    December

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    35

  • Pages from-to

    9

  • UT code for WoS article

    001137473500001

  • EID of the result in the Scopus database