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Volumn 45, Issue 1, 1998, Pages 70-122

Probabilistic checking of proofs: A new characterization of NP

Author keywords

F.1.2 Computation by Abstract Devices : Modes of Computation; F.1.3 Computation by Abstract Devices : Complexity Classes; F.2.1 Analysis of Algorithms and Problem Complexity : Numerical Algorithms and Problems

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ERROR CORRECTION; FORMAL LOGIC; POLYNOMIALS; PROBABILITY; SET THEORY; THEOREM PROVING;

EID: 0031651077     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/273865.273901     Document Type: Article
Times cited : (891)

References (55)
  • 2
    • 84990678058 scopus 로고
    • Simple constructions of almost k-wise independent random variables
    • ALON, N., GOLDREICH, O., HASTAD, J., AND PERALTA, R. 1992. Simple constructions of almost k-wise independent random variables. Rand. Struct. Algor. 3, 3, 289-304.
    • (1992) Rand. Struct. Algor. , vol.3 , Issue.3 , pp. 289-304
    • Alon, N.1    Goldreich, O.2    Hastad, J.3    Peralta, R.4
  • 9
    • 0021980820 scopus 로고
    • Trading group theory for randomness
    • (Providence, R.I., May 6-8). ACM, New York
    • BABAI, L. 1985. Trading group theory for randomness. In Proceedings of the 17th ACM Symposium on Theory of Computing (Providence, R.I., May 6-8). ACM, New York, pp. 421-429.
    • (1985) Proceedings of the 17th ACM Symposium on Theory of Computing , pp. 421-429
    • Babai, L.1
  • 11
    • 0002771903 scopus 로고
    • Non-deterministic exponential time has two-prover interactive protocols
    • BABAI, L., FORTNOW, L., AND LUND, C. 1991b. Non-deterministic exponential time has two-prover interactive protocols. Comput. Comp. 1, 3-40.
    • (1991) Comput. Comp. , vol.1 , pp. 3-40
    • Babai, L.1    Fortnow, L.2    Lund, C.3
  • 12
    • 0013117132 scopus 로고
    • Interactive proofs and approximation: Reductions from two provers in one round
    • IEEE Computer Press, New York
    • BELLARE, M. 1993. Interactive proofs and approximation: Reductions from two provers in one round. In Proceedings of the 2nd Israel Symposium on Theory and Computing Systems. IEEE Computer Press, New York, pp. 266-274.
    • (1993) Proceedings of the 2nd Israel Symposium on Theory and Computing Systems , pp. 266-274
    • Bellare, M.1
  • 14
    • 84945961823 scopus 로고
    • Efficient probabilistically checkable proofs with applications to approximation
    • (San Diego, Calif., May 16-18). ACM, New York, Errata in Proceedings of the 26th Annual ACM Symposium on Theory of Computing, p. 820
    • BELLARE, M., GOLDWASSER, S., LUND, C., AND RUSSELL, A. 1993. Efficient probabilistically checkable proofs with applications to approximation. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing (San Diego, Calif., May 16-18). ACM, New York, pp. 113-131. (Errata in Proceedings of the 26th Annual ACM Symposium on Theory of Computing, p. 820.)
    • (1993) Proceedings of the 25th Annual ACM Symposium on Theory of Computing , pp. 113-131
    • Bellare, M.1    Goldwasser, S.2    Lund, C.3    Russell, A.4
  • 15
    • 0345581486 scopus 로고
    • The complexity of approximating nonlinear programs
    • P. M. Pardalos, ed. World Scientific
    • BELLARE, M., AND ROGAWAY, P. 1993. The complexity of approximating nonlinear programs. In Complexity of Numerical Optimization, P. M. Pardalos, ed. World Scientific.
    • (1993) Complexity of Numerical Optimization
    • Bellare, M.1    Rogaway, P.2
  • 21
    • 0001159084 scopus 로고
    • Approximating maximum independent sets by excluding subgraphs
    • BOPPANA, R., AND HALLDÓRSSON, M. 1992. Approximating maximum independent sets by excluding subgraphs. BIT 32, 180-196.
    • (1992) BIT , vol.32 , pp. 180-196
    • Boppana, R.1    Halldórsson, M.2
  • 23
    • 0002739272 scopus 로고
    • On the power of two-point based sampling
    • CHOR, B., AND GOLDREICH, O. 1989, On the power of two-point based sampling. J. Complex. 5, 96-106.
    • (1989) J. Complex. , vol.5 , pp. 96-106
    • Chor, B.1    Goldreich, O.2
  • 24
    • 0348080435 scopus 로고
    • The complexity of the max-word problem and the power of one-way interactive proof systems
    • CONDON, A. 1993. The complexity of the max-word problem and the power of one-way interactive proof systems. Computat. Complex. 3, 292-305.
    • (1993) Computat. Complex. , vol.3 , pp. 292-305
    • Condon, A.1
  • 27
    • 85059770931 scopus 로고
    • The complexity of theorem-proving procedures
    • (Shaker Heights, Oh., May 3-5). ACM, New York
    • COOK, S. A. 1971. The complexity of theorem-proving procedures. In Proceedings of the 3rd Annual ACM Symposium on Theory of Computing (Shaker Heights, Oh., May 3-5). ACM, New York, pp. 151-158.
    • (1971) Proceedings of the 3rd Annual ACM Symposium on Theory of Computing , pp. 151-158
    • Cook, S.A.1
  • 28
    • 0002188798 scopus 로고
    • Generalized first-order spectra and polynomial-time recognizable sets
    • Richard Karp, ed. AMS, Providence, R.I.
    • FAGIN, R. 1974. Generalized first-order spectra and polynomial-time recognizable sets. In Complexity of Computer Computations, Richard Karp, ed. AMS, Providence, R.I., pp. 43-73.
    • (1974) Complexity of Computer Computations , pp. 43-73
    • Fagin, R.1
  • 30
    • 0026991175 scopus 로고
    • Two-prover one-round proof systems: Their power and their problems
    • (Victoria, B.C., Canada, May 4-6). ACM, New York
    • FEIGE, U., AND LOVÁSZ, L. 1992. Two-prover one-round proof systems: Their power and their problems. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing (Victoria, B.C., Canada, May 4-6). ACM, New York, pp. 733-741.
    • (1992) Proceedings of the 24th Annual ACM Symposium on Theory of Computing , pp. 733-741
    • Feige, U.1    Lovász, L.2
  • 32
    • 0024057387 scopus 로고
    • Are there interactive protocols for co-np languages?
    • FORTNOW, L., AND SIPSER, M. 1988. Are there interactive protocols for co-np languages? Inf. Proc. Lett. 28, 249-251.
    • (1988) Inf. Proc. Lett. , vol.28 , pp. 249-251
    • Fortnow, L.1    Sipser, M.2
  • 33
    • 0024611659 scopus 로고
    • The knowledge complexity of interactive proofs
    • GOLDWASSER, S., MICALI, S., AND RACKOFF, C. 1989. The knowledge complexity of interactive proofs. SIAM J. Comput. 18, 186-208.
    • (1989) SIAM J. Comput. , vol.18 , pp. 186-208
    • Goldwasser, S.1    Micali, S.2    Rackoff, C.3
  • 36
    • 0003037529 scopus 로고
    • Reducibility among combinatorial problems
    • Miller and Thatcher, eds. Plenum Press, New York
    • KARP, R. M. 1972. Reducibility among combinatorial problems. In Complexity of Computer Computations, Miller and Thatcher, eds. Plenum Press, New York, pp. 85-103.
    • (1972) Complexity of Computer Computations , pp. 85-103
    • Karp, R.M.1
  • 40
    • 0000202647 scopus 로고
    • Universal'nyǐe perebornyǐe zadachi
    • LEVIN, L. 1973. Universal'nyǐe perebornyǐe zadachi (universal search problems: in Russian). Prob. Per. Inf. 9, 3, 265-266.
    • (1973) Prob. Per. Inf. , vol.9 , Issue.3 , pp. 265-266
    • Levin, L.1
  • 42
    • 0026930922 scopus 로고
    • Algebraic methods for interactive proof systems
    • LUND, C., FORTNOW, L., KARLOFF, H., AND NISAN, N. 1992. Algebraic methods for interactive proof systems. J. ACM, 39, 4 (Oct.), 859-868.
    • (1992) J. ACM , vol.39 , Issue.4 OCT. , pp. 859-868
    • Lund, C.1    Fortnow, L.2    Karloff, H.3    Nisan, N.4
  • 43
    • 0028514351 scopus 로고
    • On the hardness of approximating minimization problems
    • LUND, C., AND YANNAKAKIS, M. 1994. On the hardness of approximating minimization problems. J. ACM, 41, 5 (Sept.), 960-981.
    • (1994) J. ACM , vol.41 , Issue.5 SEPT. , pp. 960-981
    • Lund, C.1    Yannakakis, M.2
  • 44
    • 0027641832 scopus 로고
    • Small-bias probability spaces: Efficient constructions and applications
    • NAOR, J., AND NAOR, M. 1993. Small-bias probability spaces: efficient constructions and applications. Siam J. Comput., 22, 838-856.
    • (1993) Siam J. Comput. , vol.22 , pp. 838-856
    • Naor, J.1    Naor, M.2
  • 46
    • 0026366408 scopus 로고
    • Optimization, approximation and complexity classes
    • PAPADIMITRIOU, C., AND YANNAKAKIS, M. 1991. Optimization, approximation and complexity classes. J. Comput. Syst. Sci. 43, 425-440.
    • (1991) J. Comput. Syst. Sci. , vol.43 , pp. 425-440
    • Papadimitriou, C.1    Yannakakis, M.2
  • 49
    • 0030714232 scopus 로고    scopus 로고
    • A sub-constant error-probability low-degree test and a sub-constant error-probability PCP characterization of NP
    • (El Paso, Tex., May 4-6). ACM, New York
    • RAZ, R., AND SAFRA, S. 1997. A sub-constant error-probability low-degree test and a sub-constant error-probability PCP characterization of NP. In Proceedings of the 29th Annual ACM Symposium on Theory of Computing (El Paso, Tex., May 4-6). ACM, New York, pp. 475-484.
    • (1997) Proceedings of the 29th Annual ACM Symposium on Theory of Computing , pp. 475-484
    • Raz, R.1    Safra, S.2
  • 50
    • 85029508009 scopus 로고
    • Self-testing polynomial functions efficiently and over rational domains
    • (Orlando, Fla., Jan. 27-29). ACM, New York
    • RUBINFELD, R., AND SUDAN, M. 1992. Self-testing polynomial functions efficiently and over rational domains. In Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms (Orlando, Fla., Jan. 27-29). ACM, New York, pp. 23-32.
    • (1992) Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms , pp. 23-32
    • Rubinfeld, R.1    Sudan, M.2
  • 51
    • 0026930543 scopus 로고
    • IP = PSPACE
    • SHAMIR, A. 1992. IP = PSPACE. J. ACM, 39, 4 (Oct.), 869-877.
    • (1992) J. ACM , vol.39 , Issue.4 OCT. , pp. 869-877
    • Shamir, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.