NP is as easy as detecting unique solutions
Theoretical Computer Science
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Matching is as easy as matrix inversion
Combinatorica
Small-bias probability spaces: efficient constructions and applications
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Randomized polynomials, threshold circuits, and the polynomial hierarchy
STACS 91 Proceedings of the 8th annual symposium on Theoretical aspects of computer science
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Counting classes are at least as hard as the polynomial-time hierarchy
SIAM Journal on Computing
The computational complexity of universal hashing
Theoretical Computer Science - Special issue on structure in complexity theory
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Determinism, nondeterminism, alternation, and counting
Determinism, nondeterminism, alternation, and counting
A Uniform Circuit Lower Bound For the Permanent
SIAM Journal on Computing
Randomness as a computational resource: issues in efficient computation
Randomness as a computational resource: issues in efficient computation
Polynomials and combinatorial definitions of languages
Complexity theory retrospective II
On the computational power of PP and (+)P
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
A note on the power of threshold circuits
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
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Naor and Naor [11] implicitly isolate an odd number of elements of a nonempty set of n -bit vectors. We perform a tighter analysis of their construction and obtain better probability bounds. Using this construction, we improve bounds on several results in complexity theory that originally used a construction due to Valiant and Vazirani [18]. In particular, we obtain better bounds on polynomials which approximate boolean functions; improve bounds on the running time of the 驴 P machine in Toda's result [16]; and improve bounds on the size of threshold circuits accepting languages accepted by AC 0 circuits.