Hardness amplification within NP
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Boosting and Hard-Core Set Construction
Machine Learning
On the Representation of Boolean Predicates of the Diffie-Hellman Function
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Threshold circuit lower bounds on cryptographic functions
Journal of Computer and System Sciences
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Chernoff-type direct product theorems
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
A strong direct product theorem for disjointness
Proceedings of the forty-second ACM symposium on Theory of computing
Optimal direct sum results for deterministic and randomized decision tree complexity
Information Processing Letters
Choosing, agreeing, and eliminating in communication complexity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Quantum and classical communication-space tradeoffs from rectangle bounds
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Choosing, Agreeing, and Eliminating in Communication Complexity
Computational Complexity
| Hi-index | 0.00 |
Institute for Advanced StudyAbstract: A fundamental question of complexity theory is the direct product question. A famous example is Yao's XOR-lemma, [19] in which one assumes that some function f is hard on average for small circuits, (meaning that every circuit of some fixed size s which attempts to compute f is wrong on a non-negligible fraction of the inputs) and concludes that every circuit of size s^\prime has a small advantage over guessing randomly when computing f^{\oplus k}(x_1,\cdots , x_k )=f(x_1)\oplus\cdots \oplus f(x_k) on independently chosen x_1,\cdots , x_k. All known proofs of this lemma, [12, 6, 8, 5] have the feature that s^\prime