Polynomial Representations of Symmetric Partial Boolean Functions

For Boolean polynomials in $\mathbb{Z}_p$ of sufficiently low degree we derive a relation expressing their values on one level set in terms of their values on another level set. We use this relation to derive linear upper and lower bounds, tight to within constant factor, on the degrees of various a...

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Vydáno v:SIAM journal on discrete mathematics Ročník 19; číslo 2; s. 481 - 488
Hlavní autoři: de Graaf, Mart, Valiant, Paul
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2005
Témata:
Boolean
Codes
Polynomials
ISSN:0895-4801, 1095-7146
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Shrnutí:For Boolean polynomials in $\mathbb{Z}_p$ of sufficiently low degree we derive a relation expressing their values on one level set in terms of their values on another level set. We use this relation to derive linear upper and lower bounds, tight to within constant factor, on the degrees of various approximate majority functions, namely, functions that take the value 0 on one level set, the value 1 on a different level set, and arbitrary 0-1 values on other Boolean inputs. We show sublinear upper bounds in the case of moduli that are not prime powers.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0895-4801
1095-7146
DOI:10.1137/S0895480103433562