One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
Random-self-reducibility of complete sets
SIAM Journal on Computing
BPP has subexponential time simulations unless EXPTIME has publishable proofs
Computational Complexity
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
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
Randomness vs time: derandomization under a uniform assumption
Journal of Computer and System Sciences
Boosting and Hard-Core Set Construction
Machine Learning
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
List-Decoding Using The XOR Lemma
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Hardness amplification within NP
Journal of Computer and System Sciences - Special issue on computational complexity 2002
Simple extractors for all min-entropies and a new pseudorandom generator
Journal of the ACM (JACM)
On uniform amplification of hardness in NP
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The complexity of constructing pseudorandom generators from hard functions
Computational Complexity
On Constructing Parallel Pseudorandom Generators from One-Way Functions
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Using Nondeterminism to Amplify Hardness
SIAM Journal on Computing
On basing one-way functions on NP-hardness
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Distinguishing SAT from Polynomial-Size Circuits, through Black-Box Queries
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Verifying and decoding in constant depth
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On Worst-Case to Average-Case Reductions for NP Problems
SIAM Journal on Computing
Hardness Amplification for Errorless Heuristics
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
If NP Languages are Hard on the Worst-Case, Then it is Easy to Find Their Hard Instances
Computational Complexity
Pseudorandomness and Average-Case Complexity Via Uniform Reductions
Computational Complexity
The Complexity of Local List Decoding
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Limitations of Hardness vs. Randomness under Uniform Reductions
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Worst-Case to Average-Case Reductions Revisited
APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Hardness Amplification via Space-Efficient Direct Products
Computational Complexity
Chernoff-Type Direct Product Theorems
Journal of Cryptology
Approximate List-Decoding of Direct Product Codes and Uniform Hardness Amplification
SIAM Journal on Computing
Hardness amplification within NP against deterministic algorithms
Journal of Computer and System Sciences
Uniform Direct Product Theorems: Simplified, Optimized, and Derandomized
SIAM Journal on Computing
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
Complexity of Hard-Core Set Proofs
Computational Complexity
Studies in complexity and cryptography
Query complexity in errorless hardness amplification
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
On the Complexity of Hardness Amplification
IEEE Transactions on Information Theory
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Hardness amplification results show that for every Boolean function f, there exists a Boolean function Amp(f) such that if every size s circuit computes f correctly on at most a 1 驴 驴 fraction of inputs, then every size s驴 circuit computes Amp(f) correctly on at most a $${1/2+\epsilon}$$ fraction of inputs. All hardness amplification results in the literature suffer from "size loss" meaning that $${s' \leq \epsilon \cdot s}$$ . We show that proofs using "non-uniform reductions" must suffer from such size loss.A reduction is an oracle circuit $${R^{(\cdot)}}$$ which given oracle access to any function D that computes Amp(f) correctly on a $${1/2+\epsilon}$$ fraction of inputs, computes f correctly on a 1 驴 驴 fraction of inputs. A non-uniform reduction is allowed to also receive a short advice string that may depend on both f and D. The well-known connection between hardness amplification and list-decodable error-correcting codes implies that reductions showing hardness amplification cannot be uniform for $${\epsilon . We show that every non-uniform reduction must make at least $${\Omega(1/\epsilon)}$$ queries to its oracle, which implies size loss. Our result is the first lower bound that applies to non-uniform reductions that are adaptive, whereas previous bounds by Shaltiel & Viola (SICOMP 2010) applied only to non-adaptive reductions. We also prove similar bounds for a stronger notion of "function-specific" reductions in which the reduction is only required to work for a specific function f.