The DOI matches its Crossref record; 61 of the 61 references it cites were found in a registry or an index.
Free bits, PCPs and non-approximability-towards tight results
Abstract
The first part of this paper presents new proof systems and improved non-approximability results. In particular we present a proof system for NP using logarithmic randomness and two amortized free bits, so that Max clique is hard within N/sup 1/3/ and chromatic number within N/sup 1/5/. We also show hardness of 38/37 for Max-3-SAT, 27/26 for vertex cover, 82/81 for Max-cut, and 94/93 for Max-2-SAT. The second part of this paper presents a "reverse" of the FGLSS connection by showing that an NP-hardness result for the approximation of Max clique to within a factor of N/sup 1/(g+1/) would imply a probabilistic verifier for NP with logarithmic randomness and amortized free-bit complexity g. We also show that "existing techniques" won't yield proof systems of less than two bits in amortized free bit complexity. Finally, we initiate a comprehensive study of PCP and FPCP parameters, proving several triviality results and providing several useful transformations.
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Cites
(1979) · Cited by 43,841
Reducibility among Combinatorial Problems
Karp, R. M. (1972) · Complexity of Computer Computations · doi:10.1007/978-1-4684-2001-2_9 · Cited by 11,511
The Theory of Error-Correcting Codes
(1977) · North-Holland Mathematical Library · doi:10.1016/s0924-6509(08)x7030-8 · Cited by 10,760
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
Motwani, R., & Raghavan, P. (1995) · Cambridge University Press eBooks · doi:10.1017/cbo9780511814075 · Cited by 5,123
Spencer, J. (1991) · Medical Entomology and Zoology · Cited by 4,310
Goemans, M. X., & Williamson, D. P. (1995) · Journal of the ACM · doi:10.1145/227683.227684 · Cited by 3,587
The knowledge complexity of interactive proof systems
Goldwasser, S., Micali, S., & Rackoff, C. (1989) · SIAM Journal on Computing · doi:10.1137/0218012 · Cited by 3,285
Some simplified NP-complete graph problems
Garey, M. R., Johnson, D. S., & Stockmeyer, L. (1976) · Theoretical Computer Science · doi:10.1016/0304-3975(76)90059-1 · Cited by 2,059
P-Complete Approximation Problems
Sahni, S., & Gonzalez, T. (1976) · Journal of the ACM · doi:10.1145/321958.321975 · Cited by 1,703
Cited by
Goemans, M. X., & Williamson, D. P. (1995) · Journal of the ACM · doi:10.1145/227683.227684 · Cited by 3,587
Probabilistic checking of proofs: a new characterization of NP
Arora, S., & Safra, S. (1998) · Journal of the ACM · doi:10.1145/273865.273901 · Cited by 1,153
Property testing and its connection to learning and approximation
Goldreich, O., Goldwasser, S., & Ron, D. (1998) · Journal of the ACM · doi:10.1145/285055.285060 · Cited by 1,020
Self-citationO'Donnell, R. (2014) · Cambridge University Press eBooks · doi:10.1017/cbo9781139814782 · Cited by 932
Boros, E., & Hammer, P. L. (2002) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(01)00341-9 · Cited by 827
Metadata
- Authors
- Bellare, M., Goldreich, O., & Sudan, M.
- Venue
- Proceedings of IEEE 36th Annual Foundations of Computer Science
- Publisher
- IEEE Comput. Soc. Press
- Published
- 2002-11-19
- Pages
- 422-431
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W2202947145
- Cited by
- 265
- References
- 61
- FWCI
- 18.48
- Type
- conference paper
- Language
- en
- Open access
- closed
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- Bellare, M., Goldreich, O., & Sudan, M. (2002). Free bits, PCPs and non-approximability-towards tight results. Proceedings of IEEE 36th Annual Foundations of Computer Science. https://doi.org/10.1109/sfcs.1995.492573
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