The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP
Abstract
We introduce a new low-degree--test, one that uses the restriction of low-degree polynomials to planes (i.e., affine sub-spaces of dimension 2), rather than the restriction to lines (i.e., affine sub-spaces of dimension 1). We prove the new test to be of a very small errorprobability (in particular, much smaller than constant). The new test enables us to prove a low-error characterization of NP in terms of PCP. Specifically, our theorem states that, for any given ffl ? 0, membership in any NP language can be verified with O(1) accesses, each reading logarithmic number of bits, and such that the error-probability is 2 \\Gamma log 1\\Gammaffl n . Our results are in fact stronger, as stated below. One application of the new characterization of NP is that approximating SET-COVER to within a logarithmic factors is NP-hard. Previous analysis for low-degree-tests, as well as previous characterizations of NP in terms of PCP, have managed to achieve, with constant number of accesses, error...
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Cites
The complexity of theorem-proving procedures
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Non-deterministic exponential time has two-prover interactive protocols
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Cited by
Korte, B., & Vygen, J. (2000) · Algorithms and Combinatorics · doi:10.1007/978-3-662-21708-5_16 · Cited by 579
Self-testing of quantum systems: a review
Šupić, I., & Bowles, J. (2020) · Quantum · doi:10.22331/q-2020-09-30-337 · Cited by 365
Succinct Non-interactive Arguments via Linear Interactive Proofs
Bitansky, N., Chiesa, A., Ishai, Y., Paneth, O., & Ostrovsky, R. (2013) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-36594-2_18 · Cited by 274
Metadata
- Authors
- Raz, R., & Safra, S.
- Venue
- Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97
- Publisher
- ACM Press
- Published
- 1997
- Pages
- 475-484
- OpenAlex
- W2003159902
- Cited by
- 834
- References
- 22
- FWCI
- 14.13
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Raz, R., & Safra, S. (1997). A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97. https://doi.org/10.1145/258533.258641
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