How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
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
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Random-self-reducibility of complete sets
SIAM Journal on Computing
Journal of Computer and System Sciences
Pseudorandomness for network algorithms
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
When do extra majority gates help?: polylog(N) majority gates are equivalent to one
Computational Complexity - Special issue on circuit complexity
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SIAM Journal on Computing
Tiny families of functions with random properties: a quality-size trade-off for hashing
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Randomness-optimal oblivious sampling
Proceedings of the workshop on Randomized algorithms and computation
On recycling the randomness of states in space bounded computation
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Pseudorandom generators without the XOR lemma
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Perfect Constant-Round Secure Computation via Perfect Randomizing Polynomials
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Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
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Succinct quantum proofs for properties of finite groups
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A theorem on probabilistic constant depth Computations
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Classical and Quantum Computation
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Unbalanced Expanders and Randomness Extractors from Parvaresh-Vardy Codes
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
Pseudorandom Bits for Constant-Depth Circuits with Few Arbitrary Symmetric Gates
SIAM Journal on Computing
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A (de)constructive approach to program checking
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Theory and application of trapdoor functions
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
On representations by low-degree polynomials
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
On Approximate Majority and Probabilistic Time
Computational Complexity
On the Power of Small-Depth Computation
Foundations and Trends® in Theoretical Computer Science
BQP and the polynomial hierarchy
Proceedings of the forty-second ACM symposium on Theory of computing
Improving exhaustive search implies superpolynomial lower bounds
Proceedings of the forty-second ACM symposium on Theory of computing
The Coin Problem and Pseudorandomness for Branching Programs
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Pseudorandom Generators for Regular Branching Programs
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
The Complexity of Distributions
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
On the complexity of hard-core set constructions
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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The hybrid argument allows one to relate the distinguishability of a distribution (from uniform) to the predictability of individual bits given a prefix. The argument incurs a loss of a factor k equal to the bit-length of the distributions: ε-distinguishability implies ε/k-predictability. This paper studies the consequences of avoiding this loss - what we call "beating the hybrid argument" -- and develops new proof techniques that circumvent the loss in certain natural settings. Specifically, we obtain the following results: 1. We give an instantiation of the Nisan-Wigderson generator (JCSS '94) that can be broken by quantum computers, and that is o(1)-unpredictable against AC0. We conjecture that this generator indeed fools AC0. Our conjecture implies the existence of an oracle relative to which BQP is not in the PH, a longstanding open problem. 2. We show that the "INW" generator by Impagliazzo, Nisan, and Wigderson (STOC '94) with seed length O(log n log log n) produces a distribution that is 1/log n-unpredictable against poly-logarithmic width (general) read-once oblivious branching programs. Obtaining such generators where the output is indistinguishable from uniform is a longstanding open problem. 3. We identify a property of functions f, "resamplability," that allows us to beat the hybrid argument when arguing indistinguishability of [EQUATION] from uniform. This gives new pseudorandom generators for classes such as AC0[p] with a stretch that, despite being sub-linear, is the largest known. We view this as a first step towards beating the hybrid argument in the analysis of the Nisan-Wigderson generator (which applies [EQUATION] on correlated x1,...,xk) and proving the conjecture in the first item.