Pseudorandom Generators for Combinatorial Checkerboards

We define a combinatorial checkerboard to be a function f : {1, . . . , m}d {1, -1} of the form f(u1, . . . , ud) = d i=1 fi(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 -fools all combinatorial checkerboards with seed length O log m + log d

• Type: Journal
• Year: 2010
• Where: ECCC
• Authors: Thomas Watson
• Keywords: Combinatorial Checkerboards, Combinatorial Rectangles, ECCC 2010, Explicit Pseudorandom Generators