One-way functions and Pseudorandom generators
Combinatorica - Theory of Computing
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
On the distributional complexity of disjointness
Theoretical Computer Science
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
Direct product results and the GCD problem, in old and new communication models
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Communication complexity
SIAM Journal on Computing
Products and Help Bits in Decision Trees
SIAM Journal on Computing
Hard-core distributions for somewhat hard problems
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Error Reduction by Parallel Repetition—A Negative Result
Combinatorica
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Amplifying collision resistance: a complexity-theoretic treatment
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
How to compress interactive communication
Proceedings of the forty-second ACM symposium on Theory of computing
Composition theorems in communication complexity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Constructive proofs of concentration bounds
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
A little advice can be very helpful
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Interactive information complexity
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Direct product via round-preserving compression
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Derandomized Parallel Repetition Theorems for Free Games
Computational Complexity
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A fundamental question of complexity theory is the direct product question. A famous example is Yao's XOR-lemma, 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' only has a small advantage over guessing randomly when computing f⊕k(x1,...,xk) = f(x1) ⊕...⊕ f(xk) on independently chosen x1,...,xk. All known proofs of this lemma have the property that s' s. In words, the circuit which attempts to compute f⊕k is smaller than the circuit which attempts to compute f on a single input! This paper addresses the issue of proving strong direct product assertions, that is, ones in which s' ≈ ks and is in particular larger than s. We study the question of proving strong direct product question for decision trees and communication protocols.