All

What are you looking for?

All
Projects
Results
Organizations

Quick search

  • Projects supported by TA ČR
  • Excellent projects
  • Projects with the highest public support
  • Current projects

Smart search

  • That is how I find a specific +word
  • That is how I leave the -word out of the results
  • “That is how I can find the whole phrase”

En route to the log-rank conjecture: new reductions and equivalent formulations

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F14%3A00434135" target="_blank" >RIV/67985840:_____/14:00434135 - isvavai.cz</a>

  • Result on the web

    <a href="http://dx.doi.org/10.1007/978-3-662-43948-7_43" target="_blank" >http://dx.doi.org/10.1007/978-3-662-43948-7_43</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/978-3-662-43948-7_43" target="_blank" >10.1007/978-3-662-43948-7_43</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    En route to the log-rank conjecture: new reductions and equivalent formulations

  • Original language description

    We prove that several measures in communication complexity are equivalent, up to polynomial factors in the logarithm of the rank of the associated matrix: deterministic communication complexity, randomized communication complexity, information cost and zero-communication cost. This shows that in order to prove the log-rank conjecture, it suffices to show that low-rank matrices have efficient protocols in any of the aforementioned measures. Furthermore, we show that the notion of zero-communication complexity is equivalent to an extension of the common discrepancy bound. Linial et al. [Combinatorica, 2007] showed that the discrepancy of a sign matrix is lower-bounded by an inverse polynomial in the logarithm of the associated matrix. We show that if these results can be generalized to the extended discrepancy, this will imply the log-rank conjecture.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2014

  • Confidentiality

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

Data specific for result type

  • Article name in the collection

    Automata, Languages, and Programming

  • ISBN

    978-3-662-43947-0

  • ISSN

  • e-ISSN

  • Number of pages

    11

  • Pages from-to

    514-524

  • Publisher name

    Springer

  • Place of publication

    Berlin

  • Event location

    Copenhagen

  • Event date

    Jul 8, 2014

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article

    000352643300045