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- W2129570070 abstract "We define a combinatorial checkerboard to be a function $f:{1,ldots,m}^dto{1,-1}$ of the form $f(u_1,ldots,u_d)=prod_{i=1}^df_i(u_i)$ for some functions $f_i:{1,ldots,m}to{1,-1}$. This is a variant of combinatorial rectangles, which can be defined in the same way but using ${0,1}$ instead of ${1,-1}$. We consider the problem of constructing explicit pseudorandom generators for combinatorial checkerboards. This is a generalization of small-bias generators, which correspond to the case $m=2$. We construct a pseudorandom generator that $epsilon$-fools all combinatorial checkerboards with seed length $Obigl(log m+log dcdotloglog d+log^{3/2}frac{1}{epsilon}bigr)$. Previous work by Impagliazzo, Nisan, and Wigderson implies a pseudorandom generator with seed length $Obigl(log m+log^2d+log dcdotlogfrac{1}{epsilon}bigr)$. Our seed length is better except when $frac{1}{epsilon}geq d^{omega(log d)}$." @default.
- W2129570070 created "2016-06-24" @default.
- W2129570070 creator A5004743191 @default.
- W2129570070 date "2011-06-01" @default.
- W2129570070 modified "2023-09-26" @default.
- W2129570070 title "Pseudorandom Generators for Combinatorial Checkerboards" @default.
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- W2129570070 doi "https://doi.org/10.1109/ccc.2011.12" @default.
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