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PowerPoint presentation by Madhu Sudan
Presentation by Madhu Sudan
- Arora, S., Babai, L., Stern, J., Sweedyk, Z. The hardness of approximate optima in lattices, codes and systems of linear equations. J. Comput. Syst. Sci. 54, 2 (Apr. 1997), 317--331. Google ScholarDigital Library
- Arora, S., Lund, C. Hardness of approximations. Approximation Algorithms for NP-Hard Problems. D.S. Hochbaum, ed. PWS, 1995. Google ScholarDigital Library
- Arora, S., Lund, C., Motwani, R., Sudan, M., Szegedy, M. Proof verification and the hardness of approximation problems. J. ACM 45, 3 (May 1998), 501--555. Google ScholarDigital Library
- Arora, S., Safra, S. Probabilistic checking of proofs: A new characterization of NP. J. ACM 45, 1 (Jan. 1998), 70--122. Google ScholarDigital Library
- Babai, L., Fortnow, L., Levin, L.A., Szegedy, M. Checking computations in polylogarithmic time. In Proceedings of the 23rd ACM Symposium on the Theory of Computing (New York, 1991), ACM, 21--32. Google ScholarDigital Library
- Babai, L., Fortnow, L., Lund, C. Non-deterministic exponential time has two-prover interactive protocols. Comput. Complexity 1, 1 (1991), 3--40.Google ScholarCross Ref
- Babai, L., Moran, S. Arthur-Merlin games: A randomized proof system, and a hierarchy of complexity class. J. Comput. Syst. Sci. 36, 2 (Apr. 1988), 254--276. Google ScholarDigital Library
- Ben-Or, M., Goldwasser, S., Kilian, J., Wigderson, A. Multi-prover interactive proofs: How to remove intractability. In Proceedings of the 20th Annual ACM Symposium on the Theory of Computing (1988), 113--131. Google ScholarDigital Library
- Ben-Sasson, E., Sudan, M. Short PCPs with poly-log rate and query complexity. In Proceedings of the 37th Annual ACM Symposium on Theory of Computing (New York, 2005), ACM, 266--275. Google ScholarDigital Library
- Cohen, A., Wigderson, A. Dispersers, deterministic amplification, and weak random sources (extended abstract). In IEEE Symposium on Foundations of Computer Science (1989), 14--19. Google ScholarDigital Library
- Cook, S.A. The complexity of theorem-proving procedures. In Proceedings of the 3rd ACM Symposium Theory of Computing (Ohio, 1971), Shaker Heights, 151--158. Google ScholarDigital Library
- Dinur, I. The PCP theorem by gap amplification. In Proceedings of the 38th Annual ACM Symposium on Theory of Computing (New York, 2006), ACM, 241--250. Preliminary version appeared as an ECCC Technical Report TR05-046. Google ScholarDigital Library
- Dinur, I., Reingold, O. Assignment testers: Towards a combinatorial proof of the PCP-theorem. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (Loc Alamitos, CA, USA, 2004), IE, 155--164. Google ScholarDigital Library
- Feige, U. A threshold of ln n for approximating set cover. J. ACM 45, 4 (1998), 634--652. Google ScholarDigital Library
- Feige, U., Goldwasser, S., Lov´sz, L., Safra, S., Szegedy, M. Interactive proofs and the hardness of approximating cliques. J. ACM 43, 2 (1996), 268--292. Google ScholarDigital Library
- Fortnow, L., Rompel, J., Sipser, M. On the power of multi-prover interactive protocols. Theor. Comput. Sci. 134, 2 (1994), 545--557. Google ScholarDigital Library
- Garey, M.A., Johnson, D.S. Computers and Intractability. Freeman, 1979.Google ScholarDigital Library
- Goldreich, O. Modern Cryptography, Probabilistic Proofs and Pseudorandomness, volume 17 of Algorithms and Combinatorics. Springer-Verlag, 1998. Google ScholarDigital Library
- Goldreich, O., Micali, S., Wigderson, A. Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM 38, 1 (July 1991), 691--729. Preliminary version in IEEE FOCS, 1986. Google ScholarDigital Library
- Goldwasser, S., Micali, S., Rackoff, C. The knowledge complexity of interactive proof systems. SIAM J. Comput. 18, 1 (February 1989), 186--208. Google ScholarDigital Library
- Håstad, J. Clique is hard to approximate within n to the power 1-epsilon. Acta Mathemat. 182 (1999), 105--142.Google ScholarCross Ref
- Håstad, J. Some optimal inapproximability results. J. ACM 48 (2001),798--859. Google ScholarDigital Library
- Impagliazzo, R., Zuckerman, D. How to recycle random bits. In IEEE Symposium on Foundations of Computer Science (1989), 248--253. Google ScholarDigital Library
- Karloff, H., Zwick, U. A 7/8-approximation algorithm for max 3sat? In FOCS '97: Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS '97) (Washington, DC, USA, 1997), IEEE Computer Society, 406--415. Google ScholarDigital Library
- Karp, R.M. Reducibility among combinatorial problems. Complexity of Computer Computations. R. Miller, and J. Thatcher, eds.1972, 85--103.Google Scholar
- Khot, S. Guest column: Inapproximability results via long code based PCPs. SIGACT News 36, 2, 25--42, 2005. Google ScholarDigital Library
- Levin, L.A. Universal search problems. Problemy Peredachi Informatsii, 9, 3 (1973), 265--266.Google Scholar
- Lund, C., Fortnow, L., Karloff, H.J., Nisan, N. Algebraic methods for interactive proof systems. J. ACM 39, 4 (Oct. 1992), 859--868. Google ScholarDigital Library
- Lund, C., Yannakakis, M. On the hardness of approximating minimization problems. J. ACM 41, 5 (Sept. 1994), 960--981. Google ScholarDigital Library
- Papadimitriou, C., Yannakakis, M. Optimization, approximation, and complexity classes. J. Comput. Syst. Sci. 43 (1991), 425--440.Google ScholarCross Ref
- Radhakrishnan, J., Sudan, M. On Dinur's proof of the PCP theorem. Bulletin (New Series) Amer. Math. Soc., 44, 1 (Jan. 2007), 19--61.Google Scholar
- Raz, R. A parallel repetition theorem. SIAM J. Comput. 27, 3 (1998), 763--803. Google ScholarDigital Library
- Shamir, A. IP = PSPACE. J. ACM 39, 4 (Oct. 1992), 869--877. Google ScholarDigital Library
- Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J. 27, (1948), 379--423, 623--656.Google ScholarCross Ref
Index Terms
- Probabilistically checkable proofs
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