Deterministic simulation in LOGSPACE
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs
Journal of Computer and System Sciences
A well-characterized approximation problem
Information Processing Letters
The probabilistic method yields deterministic parallel algorithms
Proceedings of the 30th IEEE symposium on Foundations of computer science
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
&egr;-discrepancy sets and their application for interpolation of sparse polynomials
Information Processing Letters
Efficient approximation of product distributions
Random Structures & Algorithms
Journal of Computer and System Sciences - Special issue on the 36th IEEE symposium on the foundations of computer science
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Pseudorandom walks on regular digraphs and the RL vs. L problem
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Random Structures & Algorithms
Pseudorandom Bits for Polynomials
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Unconditional pseudorandom generators for low degree polynomials
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The Sum of d Small-Bias Generators Fools Polynomials of Degree d
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Randomness-efficient oblivious sampling
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Explicit construction of a small epsilon-net for linear threshold functions
Proceedings of the forty-first annual ACM symposium on Theory of computing
Small-Bias Spaces for Group Products
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Derandomized squaring of graphs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Small-Bias Spaces for Group Products
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Pseudorandom generators for combinatorial shapes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Pseudorandom generators for group products: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
The Complexity of Distributions
SIAM Journal on Computing
Pseudorandom generators for combinatorial checkerboards
Computational Complexity
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We consider the following problem: for given n ,M , produce a sequence X 1 ,X 2 ,...,X n of bits that fools every linear test modulo M . We present two constructions of generators for such sequences. For every constant prime power M , the first construction has seed length O M (log(n /*** )), which is optimal up to the hidden constant. (A similar construction was independently discovered by Meka and Zuckerman [MZ]). The second construction works for every M ,n , and has seed length O (logn + log(M /*** )log(M log(1/*** ))). The problem we study is a generalization of the problem of constructing small bias distributions [NN], which are solutions to the M = 2 case. We note that even for the case M = 3 the best previously known constructions were generators fooling general bounded-space computations, and required O (log2 n ) seed length. For our first construction, we show how to employ recently constructed generators for sequences of elements of that fool small-degree polynomials (modulo M ). The most interesting technical component of our second construction is a variant of the derandomized graph squaring operation of [RV]. Our generalization handles a product of two distinct graphs with distinct bounds on their expansion. This is then used to produce pseudorandom-walks where each step is taken on a different regular directed graph (rather than pseudorandom walks on a single regular directed graph as in [RTV, RV]).