Improved Pseudorandom Generators for Combinatorial Rectangles

Chi-Jen Lu

Abstract: We explicitly construct a pseudorandom generator which uses O(log m + log d + log3/2 1/ε) bits and approximates the volume of any combinatorial rectangle in [m]d = {1,... m}d to within ε error. This improves on the previous construction by Armoni, Saks, Wigderson, and Zhou [4] using O(log m + log d + log2 1/ε) bits. For a subclass of rectangles with at most t ≥ log 1/ε nontrivial dimensions and each dimension being an interval, we also give a pseudorandom generator using O(log log d + log 1/ε log1/2 t/log 1/ε) bits, which again improves the previous upper bound O(log log d + log 1/ε log t/log 1/ε) by Chari, Rohatgi, and Srinivasan [5].