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Probabilistic checking of proofs: a new characterization of NP
Open accessAbstract
We give a new characterization of NP: the class NP contains exactly those languages L for which membership proofs (a proof that an input x is in L ) can be verified probabilistically in polynomial time using logarithmic number of random bits and by reading sublogarithmic number of bits from the proof. We discuss implications of this characterization; specifically, we show that approximating Clique and Independent Set, even in a very weak sense, is NP-hard.
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Cites
The complexity of theorem-proving procedures
Cook, S. A. (1971) · Proceedings of the third annual ACM symposium on Theory of computing - STOC '71 · doi:10.1145/800157.805047 · Cited by 6,385
Optimization, approximation, and complexity classes
Papadimitriou, C. H., & Yannakakis, M. (1991) · Journal of Computer and System Sciences · doi:10.1016/0022-0000(91)90023-x · Cited by 1,653
Cited by
Some optimal inapproximability results
Håstad, J. (2001) · Journal of the ACM · doi:10.1145/502090.502098 · Cited by 1,902
Quantum computation and quantum-state engineering driven by dissipation
Verstraete, F., Wolf, M. M., & Ignacio Cirac, J. (2009) · Nature Physics · doi:10.1038/nphys1342 · Cited by 1,570
Universal quantum computation with ideal Clifford gates and noisy ancillas
Bravyi, S., & Kitaev, A. (2005) · Physical Review A · doi:10.1103/physreva.71.022316 · Cited by 1,525
Pinocchio: Nearly Practical Verifiable Computation
Parno, B., Howell, J., Gentry, C., & Raykova, M. (2013) · 2013 IEEE Symposium on Security and Privacy · doi:10.1109/sp.2013.47 · Cited by 864
Cube Attacks on Tweakable Black Box Polynomials
Dinur, I., & Shamir, A. (2009) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-01001-9_16 · Cited by 451
Metadata
- Authors
- Arora, S., & Safra, S.
- Venue
- Journal of the ACM
- Published
- 1998-01
- Volume
- 45
- Issue
- 1
- Pages
- 70-122
- ISSN
- 0004-5411 (ISSN-L)
- 1557-735X
- OpenAlex
- W2019578639
- Cited by
- 1,153
- References
- 2
- FWCI
- 35.16
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
