The Log-Rank Conjecture and low degree polynomials

We formulate several questions concerning the intersections of sets of Boolean roots of low degree polynomials. Two of these questions we show to be equivalent to the Log-Rank Conjecture from communication complexity. We further exhibit a slightly stronger formulation which we prove to be false, and...

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Bibliographic Details
Published inInformation processing letters Vol. 89; no. 2; pp. 99 - 103
Main Author Valiant, Paul
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 31.01.2004
Elsevier Science
Elsevier Sequoia S.A
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Boolean polynomials
Communication complexity
Computational complexity
Computer science; control theory; systems
Exact sciences and technology
Log-Rank Conjecture
Mathematical models
Studies
Theoretical computing
Log-Rank Conjecture
Boolean polynomials
Communication complexity
Computational complexity
Boolean polynomial
Log rank conjecture
Information processing
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Summary:We formulate several questions concerning the intersections of sets of Boolean roots of low degree polynomials. Two of these questions we show to be equivalent to the Log-Rank Conjecture from communication complexity. We further exhibit a slightly stronger formulation which we prove to be false, and a weaker formulation which we prove to be true. These results suggest a possible new approach to the Log-Rank Conjecture.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2003.09.020