Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
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
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences
On recycling the randomness of states in space bounded computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
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
Undirected connectivity in log-space
Journal of the ACM (JACM)
Pseudorandom Bit Generators That Fool Modular Sums
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Pseudorandom Bit Generators That Fool Modular Sums
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 group products: extended abstract
Proceedings of the forty-third annual ACM symposium on Theory of computing
A new method for constructing small-bias spaces from hermitian codes
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Pseudorandom generators for combinatorial checkerboards
Computational Complexity
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Small-bias, or *** -biased, spaces have found many applications in complexity theory, coding theory, and derandomization. We generalize the notion of small-bias spaces to the setting of group products. Besides being natural, our extension captures some of the difficulties in constructing pseudorandom generators for constant-width branching programs - a longstanding open problem. We provide an efficient deterministic construction of small-bias spaces for solvable groups. Our construction exploits the fact that solvable groups have nontrivial normal subgroups that are abelian and builds on the construction of Azar et al. [AMN98] for abelian groups. For arbitrary finite groups, we give an efficient deterministic construction achieving constant bias. We also construct pseudorandom generators fooling linear functions mod p for primes p .