Pseudorandom generators for combinatorial checkerboards
Abstract
We define a combinatorial checkerboard to be a function f: {1,⋯,m}d → {1,-1} of the form f(u1,⋯, ud) = Πi=1df(ui) for some functions fi: {1,⋯, m} → {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 ε-fools all combinatorial checkerboards with seed length O (log m + log d · log log d + log 3/2 1/ε). Previous work by Impagliazzo, Nisan, and Wigderson implies a pseudorandom generator with seed length O (log m +log2 d +log d ·log1/ε). Our seed length is better except when 1/ε ≥ d ω(log d). © 2011 IEEE.
Publication Title
Proceedings of the Annual IEEE Conference on Computational Complexity
Recommended Citation
Watson, T. (2011). Pseudorandom generators for combinatorial checkerboards. Proceedings of the Annual IEEE Conference on Computational Complexity, 232-242. https://doi.org/10.1109/CCC.2011.12
