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2008 IEEE 23rd Annual Conference on Computational Complexity
The Sum of d SmallBias Generators Fools Polynomials of Degree d
June 22June 26
ISBN: 9780769531694
ASCII Text  x  
Emanuele Viola, "The Sum of d SmallBias Generators Fools Polynomials of Degree d," 2012 IEEE 27th Conference on Computational Complexity, pp. 124127, 2008 IEEE 23rd Annual Conference on Computational Complexity, 2008.  
BibTex  x  
@article{ 10.1109/CCC.2008.16, author = {Emanuele Viola}, title = {The Sum of d SmallBias Generators Fools Polynomials of Degree d}, journal ={2012 IEEE 27th Conference on Computational Complexity}, volume = {0}, year = {2008}, issn = {10930159}, pages = {124127}, doi = {http://doi.ieeecomputersociety.org/10.1109/CCC.2008.16}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2012 IEEE 27th Conference on Computational Complexity TI  The Sum of d SmallBias Generators Fools Polynomials of Degree d SN  10930159 SP124 EP127 A1  Emanuele Viola, PY  2008 KW  null VL  0 JA  2012 IEEE 27th Conference on Computational Complexity ER   
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/CCC.2008.16
We prove that the sum of $d$ smallbias generators $L: \F^s \to \F^n$ fools degree$d$ polynomials in $n$ variables over a prime field $\F$, for any fixed degree $d$ and field $\F$, including $\F = \F_2 =\zo$. Our result improves on both the work by Bogdanov and Viola (FOCS '07) and the beautiful followup by Lovett (STOC '08). The first relies on a conjecture that turned out to be true only for some degrees and fields, while the latter considers the sum of $2^d$ smallbias generators (as opposed to $d$ in our result). Our proof builds on and somewhat simplifies the arguments by Bogdanov and Viola (FOCS '07) and by Lovett (STOC '08). Its core is a case analysis based on the \emph{bias} of the polynomial to be fooled.
Citation:
Emanuele Viola, "The Sum of d SmallBias Generators Fools Polynomials of Degree d," ccc, pp.124127, 2008 IEEE 23rd Annual Conference on Computational Complexity, 2008
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