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Hard-core distributions for somewhat hard problems
Abstract
Consider a decision problem that cannot be 1-/spl delta/ approximated by circuits of a given size in the sense that any such circuit fails to give the correct answer on at least a /spl delta/ fraction of instances. We show that for any such problem there is a specific "hard core" set of inputs which is at least a /spl delta/ fraction of all inputs and on which no circuit of a slightly smaller size can get even a small advantage over a random guess. More generally, our argument holds for any non uniform model of computation closed under majorities. We apply this result to get a new proof of the Yao XOR lemma (A.C. Yao, 1982), and to get a related XOR lemma for inputs that are only k wise independent.
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Citations
Cited by
Pseudorandom Generators without the XOR Lemma
Sudan, M., Trevisan, L., & Vadhan, S. (2001) · Journal of Computer and System Sciences · doi:10.1006/jcss.2000.1730 · Cited by 393
Extractors and pseudorandom generators
(2001) · Journal of the ACM · doi:10.1145/502090.502099 · Cited by 324
Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses
Klivans, A. R., & van Melkebeek, D. (2002) · SIAM Journal on Computing · doi:10.1137/s0097539700389652 · Cited by 270
Metadata
- Authors
- Impagliazzo, R.
- Venue
- Proceedings of IEEE 36th Annual Foundations of Computer Science
- Publisher
- IEEE Comput. Soc. Press
- Published
- 2002-11-19
- Pages
- 538-545
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2160403361
- Cited by
- 254
- References
- 0
- FWCI
- 9.85
- Type
- conference paper
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Hard-core distributions for somewhat hard problems. https://app.cochat.ai/papers/10.1109/sfcs.1995.492584
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- Impagliazzo, R. (2002). Hard-core distributions for somewhat hard problems. Proceedings of IEEE 36th Annual Foundations of Computer Science. https://doi.org/10.1109/sfcs.1995.492584
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