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Volumn 9780521884730, Issue , 2008, Pages 1-606

Computational complexity: A conceptual perspective

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EID: 84924435299     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9780511804106     Document Type: Book
Times cited : (418)

References (244)
  • 1
    • 0141438246 scopus 로고    scopus 로고
    • S. Aaronson. Complexity Zoo. A continueously updated Web site at http://qwiki.caltech.edu/wiki/ComplexityZoo/.
    • Complexity Zoo
    • Aaronson, S.1
  • 6
    • 0001011699 scopus 로고
    • A fast and simple randomized algorithm for the maximal independent set problem
    • N. Alon, L. Babai, and A. Itai. A Fast and Simple Randomized Algorithm for the Maximal Independent Set Problem. J. of Algorithms, Vol. 7, pages 567–583, 1986.
    • (1986) J. Of Algorithms , vol.7 , pp. 567-583
    • Alon, N.1    Babai, L.2    Itai, A.3
  • 7
    • 51249171493 scopus 로고
    • The monotone circuit complexity of boolean functions
    • N. Alon and R. Boppana. The Monotone Circuit Complexity of Boolean Functions. Combinatorica, Vol. 7 (1), pages 1–22, 1987.
    • (1987) Combinatorica , vol.7 , Issue.1 , pp. 1-22
    • Alon, N.1    Boppana, R.2
  • 8
    • 0026834814 scopus 로고
    • Construction of asymptotically good, low-rate error-correcting codes through pseudo-random graphs
    • N. Alon, J. Bruck, J. Naor, M. Naor, and R. Roth. Construction of Asymptotically Good, Low-Rate Error-Correcting Codes Through Pseudo-Random Graphs. IEEE Transactions on Information Theory, Vol. 38, pages 509–516, 1992.
    • (1992) IEEE Transactions on Information Theory , vol.38 , pp. 509-516
    • Alon, N.1    Bruck, J.2    Naor, J.3    Naor, M.4    Roth, R.5
  • 10
    • 84990678058 scopus 로고
    • Simple constructions of almost k-wise independent random variables
    • Preliminary version in 31st FOCS, 1990
    • N. Alon, O. Goldreich, J. Håstad, and R. Peralta. Simple Constructions of Almost k-wise Independent Random Variables. Journal of Random Structures and Algorithms, Vol. 3 (3), pages 289–304, 1992. Preliminary version in 31st FOCS, 1990.
    • (1992) Journal of Random Structures and Algorithms , vol.3 , Issue.3 , pp. 289-304
    • Alon, N.1    Goldreich, O.2    Håstad, J.3    Peralta, R.4
  • 12
    • 84924442885 scopus 로고    scopus 로고
    • On the derandomization of space-bounded computations
    • Springer-Verlag Lecture Notes in Computer Science
    • R. Armoni. On the Derandomization of Space-Bounded Computations. In the proceedings of Random 98, Springer-Verlag Lecture Notes in Computer Science (Vol. 1518), pages 49–57, 1998.
    • (1998) The Proceedings of Random 98 , vol.1518 , pp. 49-57
    • Armoni, R.1
  • 13
    • 4544261402 scopus 로고    scopus 로고
    • Approximation schemes for np-hard geometric optimization problems: A survey
    • July
    • S. Arora. Approximation Schemes for NP-Hard Geometric Optimization Problems: A Survey. Math. Programming, Vol. 97, pages 43–69, July 2003.
    • (2003) Math. Programming , vol.97 , pp. 43-69
    • Arora, S.1
  • 15
    • 0032058198 scopus 로고    scopus 로고
    • Proof Verification and Intractability of Approximation Problems
    • Preliminary version in 33rd FOCS, 1992
    • S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof Verification and Intractability of Approximation Problems. Journal of the ACM, Vol. 45, pages 501–555, 1998. Preliminary version in 33rd FOCS, 1992.
    • (1998) Journal of the ACM , vol.45 , pp. 501-555,
    • Arora, S.1    Lund, C.2    Motwani, R.3    Sudan, M.4    Szegedy, M.5
  • 16
    • 0031651077 scopus 로고    scopus 로고
    • Probabilistic checkable proofs: A new characterization of np
    • Preliminary version in 33rd FOCS, 1992
    • S. Arora and S. Safra. Probabilistic Checkable Proofs: A New Characterization of NP. Journal of the ACM, Vol. 45, pages 70–122, 1998. Preliminary version in 33rd FOCS, 1992.
    • (1998) Journal of the ACM , vol.45 , pp. 70-122
    • Arora, S.1    Safra, S.2
  • 19
    • 0023414653 scopus 로고
    • Random oracles separate pspace from the polynomial-time hierarchy
    • L. Babai. Random Oracles Separate PSPACE from the Polynomial-Time Hierarchy. Information Processing Letters, Vol. 26, pages 51–53, 1987.
    • (1987) Information Processing Letters , vol.26 , pp. 51-53
    • Babai, L.1
  • 21
    • 0002771903 scopus 로고
    • Non-deterministic exponential time has two-prover interactive protocols
    • Preliminary version in 31st FOCS, 1990
    • L. Babai, L. Fortnow, and C. Lund. Non-Deterministic Exponential Time Has Two-Prover Interactive Protocols. Computational Complexity, Vol. 1 (1), pages 3–40, 1991. Preliminary version in 31st FOCS, 1990.
    • (1991) Computational Complexity , vol.1 , Issue.1 , pp. 3-40
    • Babai, L.1    Fortnow, L.2    Lund, C.3
  • 22
    • 0001338853 scopus 로고
    • Bpp has subexponential time simulations unless exptime has publishable proofs
    • L. Babai, L. Fortnow, N. Nisan, and A. Wigderson. BPP Has Subexponential Time Simulations Unless EXPTIME Has Publishable Proofs. Complexity Theory, Vol. 3, pages 307–318, 1993.
    • (1993) Complexity Theory , vol.3 , pp. 307-318
    • Babai, L.1    Fortnow, L.2    Nisan, N.3    Wigderson, A.4
  • 23
    • 0023995534 scopus 로고
    • Arthur-merlin games: A randomized proof system and a hierarchy of complexity classes
    • L. Babai and S. Moran. Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes. Journal of Computer and System Science, Vol. 36, pages 254–276, 1988.
    • (1988) Journal of Computer and System Science , vol.36 , pp. 254-276
    • Babai, L.1    Moran, S.2
  • 26
    • 0005478995 scopus 로고
    • The complexity of partial derivatives
    • W. Baur and V. Strassen. The Complexity of Partial Derivatives. Theor. Comput. Sci. 22, pages 317–330, 1983.
    • (1983) Sci , vol.22 , pp. 317-330
    • Baur, W.1    Strassen, V.2
  • 28
    • 0034672929 scopus 로고    scopus 로고
    • Uniform generation of np-witnesses using an np-oracle
    • M. Bellare, O. Goldreich, and E. Petrank. Uniform Generation of NP-Witnesses Using an NP-Oracle. Information and Computation, Vol. 163, pages 510–526, 2000.
    • (2000) Information and Computation , vol.163 , pp. 510-526
    • Bellare, M.1    Goldreich, O.2    Petrank, E.3
  • 29
    • 0542423500 scopus 로고    scopus 로고
    • Free bits, pcps and non-approximability – towards tight results
    • Extended abstract in 36th FOCS, 1995
    • M. Bellare, O. Goldreich, and M. Sudan. Free Bits, PCPs and Non-Approximability – Towards Tight Results. SIAM Journal on Computing, Vol. 27 (3), pages 804–915, 1998. Extended abstract in 36th FOCS, 1995.
    • (1998) SIAM Journal on Computing , vol.27 , Issue.3 , pp. 804-915
    • Bellare, M.1    Goldreich, O.2    Sudan, M.3
  • 31
    • 84870216371 scopus 로고
    • 2nd Israel Symp. on, IEEE Computer Society Press
    • A. Ben-Dor and S. Halevi. In 2nd Israel Symp. on Theory of Computing and Systems, IEEE Computer Society Press, pages 108-117, 1993.
    • (1993) Theory of Computing and Systems , pp. 108-117
    • Ben-Dor, A.1    Halevi, S.2
  • 35
    • 34547829716 scopus 로고    scopus 로고
    • Robust pcps of proximity, shorter pcps, and applications to coding
    • Extended abstract in 36th STOC, 2004
    • E. Ben-Sasson, O. Goldreich, P. Harsha, M. Sudan, and S. Vadhan. Robust PCPs of Proximity, Shorter PCPs, and Applications to Coding. SIAM Journal on Computing, Vol. 36 (4), pages 889–974, 2006. Extended abstract in 36th STOC, 2004.
    • (2006) SIAM Journal on Computing , vol.36 , Issue.4 , pp. 889-974
    • Ben-Sasson, E.1    Goldreich, O.2    Harsha, P.3    Sudan, M.4    Vadhan, S.5
  • 37
    • 0001388818 scopus 로고
    • On isomorphisms and density of np and other complete sets
    • L. Berman and J. Hartmanis. On Isomorphisms and Density of NP and Other Complete Sets. SIAM Journal on Computing, Vol. 6 (2), 1977, pages 305–322.
    • (1977) SIAM Journal on Computing , vol.6 , Issue.2 , pp. 305-322
    • Berman, L.1    Hartmanis, J.2
  • 38
    • 84926396434 scopus 로고
    • A machine-independent theory of thecomplexity of recursive functions
    • M. Blum. A Machine-Independent Theory of theComplexity of Recursive Functions. Journal of the ACM, Vol. 14 (2), pages 290–305, 1967.
    • (1967) Journal of the ACM , vol.14 , Issue.2 , pp. 290-305
    • Blum, M.1
  • 40
    • 0000619172 scopus 로고
    • Self-testing/correcting with applications to numerical problems
    • M. Blum, M. Luby, and R. Rubinfeld. Self-Testing/Correcting with Applications to Numerical Problems. Journal of Computer and System Science, Vol. 47 (3), pages 549–595, 1993.
    • (1993) Journal of Computer and System Science , vol.47 , Issue.3 , pp. 549-595
    • Blum, M.1    Luby, M.2    Rubinfeld, R.3
  • 41
    • 0021522644 scopus 로고
    • How to generate cryptographically strong sequences of pseudo- random bits
    • Preliminary version in 23rd FOCS, 1982
    • M. Blum and S. Micali. How to Generate Cryptographically Strong Sequences of Pseudo- Random Bits. SIAM Journal on Computing, Vol. 13, pages 850–864, 1984. Preliminary version in 23rd FOCS, 1982.
    • (1984) SIAM Journal on Computing , vol.13 , pp. 850-864
    • Blum, M.1    Micali, S.2
  • 43
    • 34547851140 scopus 로고    scopus 로고
    • Onworst-case to average-case reductions for np problems
    • Extended abstract in 44th FOCS, 2003
    • A. Bogdanov and L. Trevisan. OnWorst-Case to Average-Case Reductions for NP Problems. SIAM Journal on Computing, Vol. 36 (4), pages 1119–1159, 2006. Extended abstract in 44th FOCS, 2003.
    • (2006) SIAM Journal on Computing , vol.36 , Issue.4 , pp. 1119-1159
    • Bogdanov, A.1    Trevisan, L.2
  • 47
    • 0015279976 scopus 로고
    • Computational complexity and the existence of complexity gaps
    • A. Borodin. Computational Complexity and the Existence of Complexity Gaps. Journal of the ACM, Vol. 19 (1), pages 158–174, 1972.
    • (1972) Journal of the ACM , vol.19 , Issue.1 , pp. 158-174
    • Borodin, A.1
  • 48
    • 0000849112 scopus 로고
    • On relating time and space to size and depth
    • A. Borodin. On Relating Time and Space to Size and Depth. SIAM Journal on Computing, Vol. 6 (4), pages 733–744, 1977.
    • (1977) SIAM Journal on Computing , vol.6 , Issue.4 , pp. 733-744
    • Borodin, A.1
  • 49
    • 0000867507 scopus 로고
    • Minimum disclosure proofs of knowledge
    • Preliminary version by Brassard and Crépeau in 27th FOCS, 1986
    • G. Brassard, D. Chaum, and C. Crépeau. Minimum Disclosure Proofs of Knowledge. Journal of Computer and System Science, Vol. 37 (2), pages 156–189, 1988. Preliminary version by Brassard and Crépeau in 27th FOCS, 1986.
    • (1988) Journal of Computer and System Science , vol.37 , Issue.2 , pp. 156-189
    • Brassard, G.1    Chaum, D.2    Crépeau, C.3
  • 51
    • 84918358658 scopus 로고
    • On the length of programs for computing finite binary sequences
    • G. J. Chaitin. On the Length of Programs for Computing Finite Binary Sequences. Journal of the ACM, Vol. 13, pages 547–570, 1966.
    • (1966) Journal of the ACM , vol.13 , pp. 547-570
    • Chaitin, G.J.1
  • 54
    • 0002739272 scopus 로고
    • On the power of two–point based sampling
    • Preliminary version dates 1985
    • B. Chor and O. Goldreich. On the Power of Two–Point Based Sampling. Jour. of Complexity, Vol. 5, pages 96–106, 1989. Preliminary version dates 1985.
    • (1989) Jour. Of Complexity , vol.5 , pp. 96-106
    • Chor, B.1    Goldreich, O.2
  • 55
    • 0000954072 scopus 로고
    • An unsolvable problem of elementary number theory
    • A. Church. An Unsolvable Problem of Elementary Number Theory. Amer. J. of Math., Vol. 58, pages 345–363, 1936.
    • (1936) Amer. J. Of Math , vol.58 , pp. 345-363
    • Church, A.1
  • 59
    • 0020766331 scopus 로고
    • An overview of computational complexity. Turing award lecture
    • S. A. Cook. An Overview of Computational Complexity. Turing Award Lecture. CACM, Vol. 26 (6), pages 401–408, 1983.
    • (1983) CACM , vol.26 , Issue.6 , pp. 401-408
    • Cook, S.A.1
  • 60
    • 0020495011 scopus 로고
    • A taxonomy of problems with fast parallel algorithms
    • S. A. Cook. A Taxonomy of Problems with Fast Parallel Algorithms. Information and Control, Vol. 64, pages 2–22, 1985.
    • (1985) Information and Control , vol.64 , pp. 2-22
    • Cook, S.A.1
  • 61
    • 0001601465 scopus 로고
    • The relative efficiency of propositional proof systems
    • S. A. Cook and R. A. Reckhow. The Relative Efficiency of Propositional Proof Systems. J. of Symbolic Logic, Vol. 44 (1), pages 36–50, 1979.
    • (1979) J. Of Symbolic Logic , vol.44 , Issue.1 , pp. 36-50
    • Cook, S.A.1    Reckhow, R.A.2
  • 62
    • 85023205150 scopus 로고
    • Matrix multiplication via arithmetic progressions
    • D. Coppersmith and S. Winograd. Matrix Multiplication via Arithmetic Progressions. Journal of Symbolic Computation, Vol. 9, pages 251–280, 1990.
    • (1990) Journal of Symbolic Computation , vol.9 , pp. 251-280
    • Coppersmith, D.1    Winograd, S.2
  • 65
    • 0000006297 scopus 로고
    • A probabilistic remark on algebraic program testing
    • R. A. DeMillo and R. J. Lipton. A Probabilistic Remark on Algebraic Program Testing. Information Processing Letters, Vol. 7 (4), pages 193–195, 1978.
    • (1978) Information Processing Letters , vol.7 , Issue.4 , pp. 193-195
    • Demillo, R.A.1    Lipton, R.J.2
  • 68
    • 34547829715 scopus 로고    scopus 로고
    • Assignment-testers: Towards a combinatorial proof of the pcptheorem
    • Extended abstract in 45th FOCS, 2004
    • I. Dinur and O. Reingold. Assignment-Testers: Towards a Combinatorial Proof of the PCPTheorem. SIAM Journal on Computing, Vol. 36 (4), pages 975–1024, 2006. Extended abstract in 45th FOCS, 2004.
    • (2006) SIAM Journal on Computing , vol.36 , Issue.4 , pp. 975-1024
    • Dinur, I.1    Reingold, O.2
  • 70
    • 0000927535 scopus 로고
    • Trees, and flowers
    • J. Edmonds. Paths, Trees, and Flowers. Canad. J. Math., Vol. 17, pages 449–467, 1965.
    • (1965) Canad. J. Math , vol.17 , pp. 449-467
    • Edmonds, J.1
  • 72
    • 0021420540 scopus 로고
    • The complexity of promise problems with applications to public-key cryptography
    • S. Even, A. L. Selman, and Y. Yacobi. The Complexity of Promise Problems with Applications to Public-Key Cryptography. Information and Control, Vol. 61, pages 159–173, 1984.
    • (1984) Information and Control , vol.61 , pp. 159-173
    • Even, S.1    Selman, A.L.2    Yacobi, Y.3
  • 74
    • 0030100766 scopus 로고    scopus 로고
    • Approximating Clique is Almost NP-Complete
    • Preliminary version in 32nd FOCS, 1991
    • U. Feige, S. Goldwasser, L. Lovász, S. Safra, and M. Szegedy. Approximating Clique is Almost NP-Complete. Journal of the ACM, Vol. 43, pages 268–292, 1996. Preliminary version in 32nd FOCS, 1991.
    • (1996) Journal of the ACM , vol.43 , pp. 268-292
    • Feige, U.1    Goldwasser, S.2    Lovász, L.3    Safra, S.4    Szegedy, M.5
  • 75
    • 0342733642 scopus 로고    scopus 로고
    • Multiple non-interactive zero-knowledge proofs under general assumptions
    • Preliminary version in 31st FOCS, 1990
    • U. Feige, D. Lapidot, and A. Shamir. Multiple Non-Interactive Zero-Knowledge Proofs Under General Assumptions. SIAM Journal on Computing, Vol. 29 (1), pages 1–28, 1999. Preliminary version in 31st FOCS, 1990.
    • (1999) SIAM Journal on Computing , vol.29 , Issue.1 , pp. 1-28
    • Feige, U.1    Lapidot, D.2    Shamir, A.3
  • 80
    • 0023728126 scopus 로고
    • On the power of multi-prover interactive protocols
    • See errata in 5th IEEE Symp. on Structure in Complexity Theory, pages 318–319, 1990
    • L. Fortnow, J. Rompel, and M. Sipser. On the Power of Multi-Prover Interactive Protocols. In 3rd IEEE Symp. on Structure in Complexity Theory, pages 156–161, 1988. See errata in 5th IEEE Symp. on Structure in Complexity Theory, pages 318–319, 1990.
    • (1988) 3Rd IEEE Symp. On Structure in Complexity Theory , pp. 156-161
    • Fortnow, L.1    Rompel, J.2    Sipser, M.3
  • 81
    • 0344918801 scopus 로고
    • A note on sparse complete sets
    • S. Fortune. A Note on Sparse Complete Sets. SIAM Journal on Computing, Vol. 8, pages 431–433, 1979.
    • (1979) SIAM Journal on Computing , vol.8 , pp. 431-433
    • Fortune, S.1
  • 83
    • 0002127588 scopus 로고
    • Parity, circuits, and the polynomial-time hierarchy
    • Preliminary version in 22nd FOCS, 1981
    • M. L. Furst, J. B. Saxe, and M. Sipser. Parity, Circuits, and the Polynomial-Time Hierarchy. Mathematical Systems Theory, Vol. 17 (1), pages 13–27, 1984. Preliminary version in 22nd FOCS, 1981.
    • (1984) Mathematical Systems Theory , vol.17 , Issue.1 , pp. 13-27
    • Furst, M.L.1    Saxe, J.B.2    Sipser, M.3
  • 84
    • 0000871697 scopus 로고
    • Explicit constructions of linear size superconcentrators
    • O. Gabber and Z. Galil. Explicit Constructions of Linear Size Superconcentrators. Journal of Computer and System Science, Vol. 22, pages 407–420, 1981.
    • (1981) Journal of Computer and System Science , vol.22 , pp. 407-420
    • Gabber, O.1    Galil, Z.2
  • 86
    • 0000319543 scopus 로고
    • Algebraic complexity theory
    • J. von zur Gathen. Algebraic Complexity Theory. Ann. Rev. Comput. Sci., Vol. 3, pages 317–347, 1988.
    • (1988) Ann. Rev. Comput. Sci , vol.3 , pp. 317-347
    • Von Zur Gathen, J.1
  • 87
    • 0003979335 scopus 로고
    • Computer Science Dept., Technion, Israel, Spring, Superseded by [91, 92]
    • O. Goldreich. Foundation of Cryptography – Class Notes. Computer Science Dept., Technion, Israel, Spring 1989. Superseded by [91, 92].
    • (1989) Foundation of Cryptography – Class Notes
    • Goldreich, O.1
  • 88
    • 0025430107 scopus 로고
    • A note on computational indistinguishability
    • (May)
    • O. Goldreich. A Note on Computational Indistinguishability. Information Processing Letters, Vol. 34 (May), pages 277–281, 1990.
    • (1990) Information Processing Letters , vol.34 , pp. 277-281
    • Goldreich, O.1
  • 90
    • 0011247227 scopus 로고    scopus 로고
    • Modern cryptography, probabilistic proofs and pseudorandomness
    • Springer
    • O. Goldreich. Modern Cryptography, Probabilistic Proofs and Pseudorandomness. Algorithms and Combinatorics Series (Vol. 17), Springer, 1999.
    • (1999) Algorithms and Combinatorics Series , vol.17
    • Goldreich, O.1
  • 95
  • 97
    • 0032108275 scopus 로고    scopus 로고
    • Property testing and its connection to learning and approximation
    • July, Extended abstract in 37th FOCS, 1996
    • O. Goldreich, S. Goldwasser, and D. Ron. Property Testing and Its Connection to Learning and Approximation. Journal of the ACM, pages 653–750, July 1998. Extended abstract in 37th FOCS, 1996.
    • (1998) Journal of the ACM , pp. 653-750
    • Goldreich, O.1    Goldwasser, S.2    Ron, D.3
  • 98
    • 0029767165 scopus 로고    scopus 로고
    • On the composition of zero-knowledge proof systems
    • Preliminary version in 17th ICALP, 1990
    • O. Goldreich and H. Krawczyk. On the Composition of Zero-Knowledge Proof Systems. SIAM Journal on Computing, Vol. 25 (1), pages 169–192, 1996. Preliminary version in 17th ICALP, 1990.
    • (1996) SIAM Journal on Computing , vol.25 , Issue.1 , pp. 169-192
    • Goldreich, O.1    Krawczyk, H.2
  • 100
    • 71149116146 scopus 로고
    • Proofs that yield nothing but their validity or all languages in np have zero-knowledge proof systems
    • Preliminary version in 27th FOCS, 1986
    • O. Goldreich, S. Micali, and A. Wigderson. Proofs That Yield Nothing but Their Validity or All Languages in NP Have Zero-Knowledge Proof Systems. Journal of the ACM, Vol. 38 (3), pages 691–729, 1991. Preliminary version in 27th FOCS, 1986.
    • (1991) Journal of the ACM , vol.38 , Issue.3 , pp. 691-729
    • Goldreich, O.1    Micali, S.2    Wigderson, A.3
  • 101
  • 103
    • 0000171993 scopus 로고    scopus 로고
    • Property testing in bounded degree graphs
    • Extended abstract in 29th STOC, 1997
    • O. Goldreich and D. Ron. Property Testing in Bounded Degree Graphs. Algorithmica, pages 302–343, 2002. Extended abstract in 29th STOC, 1997.
    • (2002) Algorithmica , pp. 302-343
    • Goldreich, O.1    Ron, D.2
  • 104
    • 0040113668 scopus 로고    scopus 로고
    • A sublinear bipartite tester for bounded degree graphs
    • Extended abstract in 30th STOC, 1998
    • O. Goldreich and D. Ron. A Sublinear Bipartite Tester for Bounded Degree Graphs. Combinatorica, Vol. 19 (3), pages 335–373, 1999. Extended abstract in 30th STOC, 1998.
    • (1999) Combinatorica , vol.19 , Issue.3 , pp. 335-373
    • Goldreich, O.1    Ron, D.2
  • 105
    • 0006238804 scopus 로고    scopus 로고
    • Learning polynomials with queries: The highly noisy case
    • O. Goldreich, R. Rubinfeld, and M. Sudan. Learning Polynomials with Queries: The Highly Noisy Case. SIAM J. Discrete Math., Vol. 13 (4), pages 535–570, 2000.
    • (2000) SIAM J. Discrete Math , vol.13 , Issue.4 , pp. 535-570
    • Goldreich, O.1    Rubinfeld, R.2    Sudan, M.3
  • 108
    • 0021409284 scopus 로고
    • Probabilistic encryption
    • Preliminary version in 14th STOC, 1982
    • S. Goldwasser and S. Micali. Probabilistic Encryption. Journal of Computer and System Science, Vol. 28 (2), pages 270–299, 1984. Preliminary version in 14th STOC, 1982.
    • (1984) Journal of Computer and System Science , vol.28 , Issue.2 , pp. 270-299
    • Goldwasser, S.1    Micali, S.2
  • 109
    • 0024611659 scopus 로고
    • The knowledge complexity of interactive proof systems
    • Preliminary version in 17th STOC, 1985. Earlier versions date to 1982
    • S. Goldwasser, S. Micali, and C. Rackoff. The Knowledge Complexity of Interactive Proof Systems. SIAM Journal on Computing, Vol. 18, pages 186–208, 1989. Preliminary version in 17th STOC, 1985. Earlier versions date to 1982.
    • (1989) SIAM Journal on Computing , vol.18 , pp. 186-208
    • Goldwasser, S.1    Micali, S.2    Rackoff, C.3
  • 110
    • 0023985465 scopus 로고
    • A digital signature scheme secure against adaptive chosen-message attacks
    • S. Goldwasser, S. Micali, and R. L. Rivest. A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks. SIAM Journal on Computing, Vol. 17, pages 281–308, 1988.
    • (1988) SIAM Journal on Computing , vol.17 , pp. 281-308
    • Goldwasser, S.1    Micali, S.2    Rivest, R.L.3
  • 111
    • 0001796243 scopus 로고
    • Private coinsversus public coins in interactive proof systems
    • (Randomness and Computation, S. Micali, ed.), Extended abstract in 18th STOC, 1986
    • S. Goldwasser and M. Sipser. Private CoinsVersus Public Coins in Interactive Proof Systems. Advances in Computing Research: A Research Annual, Vol. 5 (Randomness and Computation, S. Micali, ed.), pages 73–90, 1989. Extended abstract in 18th STOC, 1986.
    • (1989) Advances in Computing Research: A Research Annual , vol.5 , pp. 73-90
    • Goldwasser, S.1    Sipser, M.2
  • 112
    • 0004201481 scopus 로고
    • Holden-Day, 1967, (Aegean Park Press, revised edition,.)
    • S. W. Golomb. Shift Register Sequences. Holden-Day, 1967. (Aegean Park Press, revised edition, 1982.)
    • (1982) Shift Register Sequences
    • Golomb, S.W.1
  • 114
    • 84968502725 scopus 로고
    • On the computational complexity of algorithms
    • J. Hartmanis and R. E. Stearns. On the Computational Complexity of Algorithms. Transactions of the AMS, Vol. 117, pages 285–306, 1965.
    • (1965) Transactions of the AMS , vol.117 , pp. 285-306
    • Hartmanis, J.1    Stearns, R.E.2
  • 115
    • 0002343638 scopus 로고
    • Almost optimal lower bounds for small depth circuits
    • (Randomness and Computation, S. Micali, ed, Extended abstract in 18th STOC, 1986
    • J. Håastad. Almost Optimal Lower Bounds for Small Depth Circuits. Advances in Computing Research: A Research Annual, Vol. 5 (Randomness and Computation, S. Micali, ed.), pages 143–170, 1989. Extended abstract in 18th STOC, 1986.
    • (1989) Advances in Computing Research: A Research Annual , vol.5 , pp. 143-170
    • Håastad, J.1
  • 116
    • 0000109157 scopus 로고    scopus 로고
    • Clique is hard to approximate within n 1-e
    • Preliminary versions in 28th STOC (1996) and 37th FOCS (1996)
    • J. Håastad. Clique Is Hard to Approximate Within n 1-e. Acta Mathematica, Vol. 182, pages 105–142, 1999. Preliminary versions in 28th STOC (1996) and 37th FOCS (1996).
    • (1999) Acta Mathematica , vol.182 , pp. 105-142
    • Håastad, J.1
  • 117
    • 0000844603 scopus 로고    scopus 로고
    • Getting optimal in-approximability results
    • Extended abstract in 29th STOC, 1997
    • J. Håastad. Getting Optimal In-Approximability Results. Journal of the ACM, Vol. 48, pages 798–859, 2001. Extended abstract in 29th STOC, 1997.
    • (2001) Journal of the ACM , vol.48 , pp. 798-859
    • Håastad, J.1
  • 118
    • 0345253860 scopus 로고    scopus 로고
    • A pseudorandom generator from any one-way function
    • Preliminary versions by Impagliazzo et al. in 21st STOC (1989) and Håastad in 22nd STOC (1990)
    • J. Håastad, R. Impagliazzo, L. A. Levin, and M. Luby. A Pseudorandom Generator from Any One-way Function. SIAM Journal on Computing, Vol. 28 (4), pages 1364–1396, 1999. Preliminary versions by Impagliazzo et al. in 21st STOC (1989) and Håastad in 22nd STOC (1990).
    • (1999) SIAM Journal on Computing , vol.28 , Issue.4 , pp. 1364-1396
    • Håastad, J.1    Impagliazzo, R.2    Levin, L.A.3    Luby, M.4
  • 120
    • 84924461786 scopus 로고    scopus 로고
    • Computational Complexity, in press. Preliminary version in 10th RANDOM
    • A. Healy. Randomness-Efficient SamplingWithin NC1. Computational Complexity, in press. Preliminary version in 10th RANDOM, 2006.
    • (2006) Randomness-Efficient Samplingwithin NC1
    • Healy, A.1
  • 121
    • 33747154808 scopus 로고    scopus 로고
    • Using nondeterminism to amplify hardness
    • A. Healy, S. Vadhan, and E. Viola. Using Nondeterminism to Amplify Hardness. SIAM Journal on Computing, Vol. 35 (4), pages 903–931, 2006.
    • (2006) SIAM Journal on Computing , vol.35 , Issue.4 , pp. 903-931
    • Healy, A.1    Vadhan, S.2    Viola, E.3
  • 124
    • 33749002225 scopus 로고    scopus 로고
    • Expander graphs and their applications
    • S. Hoory, N. Linial, and A. Wigderson. Expander Graphs and Their Applications. Bull. AMS, Vol. 43 (4), pages 439–561, 2006.
    • (2006) Bull. AMS , vol.43 , Issue.4 , pp. 439-561
    • Hoory, S.1    Linial, N.2    Wigderson, A.3
  • 125
    • 0024091298 scopus 로고
    • Nondeterministic space is closed under complementation
    • N. Immerman. Nondeterministic Space Is Closed Under Complementation. SIAM Journal on Computing, Vol. 17, pages 760–778, 1988.
    • (1988) SIAM Journal on Computing , vol.17 , pp. 760-778
    • Immerman, N.1
  • 129
    • 0035734550 scopus 로고    scopus 로고
    • Randomness vs time: Derandomization under a uniform assumption
    • R. Impagliazzo and A. Wigderson. Randomness vs Time: Derandomization under a Uniform Assumption. Journal of Computer and System Science, Vol. 63 (4), pages 672-688, 2001.
    • (2001) Journal of Computer and System Science , vol.63 , Issue.4 , pp. 672-688
    • Impagliazzo, R.1    Wigderson, A.2
  • 131
    • 4243139497 scopus 로고    scopus 로고
    • A polynomial-time approximation algorithm for the permanent of a matrix with non-negative entries
    • M. Jerrum, A. Sinclair, and E. Vigoda. A Polynomial-Time Approximation Algorithm for the Permanent of a Matrix with Non-Negative Entries. Journal of the ACM, Vol. 51 (4), pages 671–697, 2004.
    • (2004) Journal of the ACM , vol.51 , Issue.4 , pp. 671-697
    • Jerrum, M.1    Sinclair, A.2    Vigoda, E.3
  • 132
    • 38249043088 scopus 로고
    • Random generation of combinatorial structures from a uniform distribution
    • M. Jerrum, L. Valiant, and V. V. Vazirani. Random Generation of Combinatorial Structures from a Uniform Distribution. Theoretical Computer Science, Vol. 43, pages 169–188, 1986.
    • (1986) Theoretical Computer Science , vol.43 , pp. 169-188
    • Jerrum, M.1    Valiant, L.2    Vazirani, V.V.3
  • 134
    • 15244352005 scopus 로고    scopus 로고
    • Derandomizing polynomial identity tests means proving circuit lower bounds
    • Preliminary version in 35th STOC, 2003
    • V. Kabanets and R. Impagliazzo. Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds. Computational Complexity, Vol. 13, pages 1-46, 2004. Preliminary version in 35th STOC, 2003.
    • (2004) Computational Complexity , vol.13 , pp. 1-46
    • Kabanets, V.1    Impagliazzo, R.2
  • 135
    • 84976736925 scopus 로고
    • Eigenvalues and expansion of regular graphs
    • N. Kahale. Eigenvalues and Expansion of Regular Graphs. Journal of the ACM, Vol. 42 (5), pages 1091–1106, 1995.
    • (1995) Journal of the ACM , vol.42 , Issue.5 , pp. 1091-1106
    • Kahale, N.1
  • 137
    • 0001345658 scopus 로고
    • Monotone circuits for connectivity require superlogarithmic depth
    • Preliminary version in 20th STOC, 1988
    • M. Karchmer and A. Wigderson. Monotone Circuits for Connectivity Require Superlogarithmic Depth. SIAM J. Discrete Math., Vol. 3 (2), pages 255–265, 1990. Preliminary version in 20th STOC, 1988.
    • (1990) SIAM J. Discrete Math , vol.3 , Issue.2 , pp. 255-265
    • Karchmer, M.1    Wigderson, A.2
  • 138
    • 0003037529 scopus 로고
    • Reducibility among combinatorial problems
    • R. E. Miller and J. W. Thatcher (eds.), Plenum Press
    • R. M. Karp. Reducibility Among Combinatorial Problems. In Complexity of Computer Computations, R. E. Miller and J. W. Thatcher (eds.), Plenum Press, pages 85–103, 1972.
    • (1972) Complexity of Computer Computations , pp. 85-103
    • Karp, R.M.1
  • 139
  • 140
    • 0020937083 scopus 로고
    • Andm. Luby. Monte-carlo algorithms for enumeration and reliability problems
    • R. M. Karp andM. Luby. Monte-Carlo Algorithms for Enumeration and Reliability Problems. In 24th IEEE Symposium on Foundations of Computer Science, pages 56-64, 1983.
    • (1983) 24Th IEEE Symposium on Foundations of Computer Science , pp. 56-64
    • Karp, R.M.1
  • 144
    • 0010839572 scopus 로고    scopus 로고
    • A method of determining lower bounds for the complexity of pi- schemes
    • 1971 (in Russian). English, translation in Mathematical Notes of the Academy of Sciences of the USSR, Vol. 10 (1), pages 474–479, 1971
    • V. M. Khrapchenko. A Method of Determining Lower Bounds for the Complexity of Pi- Schemes. In Matematicheskie Zametki, Vol. 10 (1), pages 83–92, 1971 (in Russian). English translation in Mathematical Notes of the Academy of Sciences of the USSR, Vol. 10 (1), pages 474–479, 1971.
    • Matematicheskie Zametki , vol.10 , Issue.1 , pp. 83-92
    • Khrapchenko, V.M.1
  • 145
    • 0026963441 scopus 로고
    • A note on efficient zero-knowledge proofs and arguments
    • J. Kilian. A Note on Efficient Zero-Knowledge Proofs and Arguments. In 24th ACM Symposium on the Theory of Computing, pages 723–732, 1992.
    • (1992) 24Th ACM Symposium on the Theory of Computing , pp. 723-732
    • Kilian, J.1
  • 146
    • 84924461784 scopus 로고
    • (Seminumerical Algorithms). Addison-Wesley, (first edition) and 1981 (second edition)
    • D. E. Knuth. The Art of Computer Programming, Vol. 2 (Seminumerical Algorithms). Addison-Wesley, 1969 (first edition) and 1981 (second edition).
    • (1969) The Art of Computer Programming , vol.2
    • Knuth, D.E.1
  • 147
    • 0001902056 scopus 로고
    • Three approaches to the concept of “the amount of information.”
    • A. Kolmogorov. Three Approaches to the Concept of “The Amount of Information.” Probl. of Inform. Transm., Vol. 1 (1), 1965.
    • (1965) Probl. Of Inform. Transm , vol.1 , Issue.1
    • Kolmogorov, A.1
  • 149
    • 0016425038 scopus 로고
    • On the structure of polynomial time reducibility
    • R. E. Ladner. On the Structure of Polynomial Time Reducibility. Journal of the ACM, Vol. 22, 1975, pages 155–171.
    • (1975) Journal of the ACM , vol.22 , pp. 155-171
    • Ladner, R.E.1
  • 150
    • 0021098038 scopus 로고
    • Bpp and the polynomial hierarchy
    • C. Lautemann. BPP and the Polynomial Hierarchy. Information Processing Letters, Vol. 17, pages 215–217, 1983.
    • (1983) Information Processing Letters , vol.17 , pp. 215-217
    • Lautemann, C.1
  • 152
    • 0002602811 scopus 로고
    • Universal search problems
    • (in Russian). English translation in Problems of Information Transmission 9, pages 265–266. A better English translation appears in [221]
    • L. A. Levin. Universal Search Problems. Problemy Peredaci Informacii 9, pages 115–116, 1973 (in Russian). English translation in Problems of Information Transmission 9, pages 265–266. A better English translation appears in [221].
    • (1973) Problemy Peredaci Informacii , vol.9 , pp. 115-116
    • Levin, L.A.1
  • 153
    • 0021404339 scopus 로고
    • Randomness conservation inequalities: Information and independence in mathematical theories
    • L. A. Levin. Randomness Conservation Inequalities: Information and Independence in Mathematical Theories. Information and Control, Vol. 61, pages 15–37, 1984.
    • (1984) Information and Control , vol.61 , pp. 15-37
    • Levin, L.A.1
  • 154
    • 0022663555 scopus 로고
    • Average case complete problems
    • L. A. Levin. Average Case Complete Problems. SIAM Journal on Computing, Vol. 15, pages 285–286, 1986.
    • (1986) SIAM Journal on Computing , vol.15 , pp. 285-286
    • Levin, L.A.1
  • 155
    • 85032413361 scopus 로고    scopus 로고
    • Fundamentals of computing. Sigact news
    • L. A. Levin. Fundamentals of Computing. SIGACT News, Education Forum, special 100th issue, Vol. 27 (3), pages 89–110, 1996.
    • (1996) Education Forum, Special 100Th Issue , vol.27 , Issue.3 , pp. 89-110
    • Levin, L.A.1
  • 157
    • 0003013846 scopus 로고
    • New directions in testing
    • J. Feigenbaum andM. Merritt (eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematics Society
    • R. J. Lipton. New Directions in Testing. Distributed Computing and Cryptography, J. Feigenbaum andM. Merritt (eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematics Society, Vol. 2, pages 191–202, 1991.
    • (1991) Distributed Computing and Cryptography , vol.2 , pp. 191-202
    • Lipton, R.J.1
  • 161
    • 33746626361 scopus 로고    scopus 로고
    • Pairwise independence and derandomization
    • Preliminary version: TR-95-035, ICSI, Berkeley, 1995
    • M. Luby and A. Wigderson. Pairwise Independence and Derandomization. Foundations and Trends in Theoretical Computer Science, Vol. (4), 2005. Preliminary version: TR-95-035, ICSI, Berkeley, 1995.
    • (2005) Foundations and Trends in Theoretical Computer Science , Issue.4
    • Luby, M.1    Wigderson, A.2
  • 162
    • 0026930922 scopus 로고
    • Algebraic methods for interactive proof systems
    • Preliminary version in 31st FOCS, 1990
    • C. Lund, L. Fortnow, H. Karloff, and N. Nisan. Algebraic Methods for Interactive Proof Systems. Journal of the ACM, Vol. 39 (4), pages 859–868, 1992. Preliminary version in 31st FOCS, 1990.
    • (1992) Journal of the ACM , vol.39 , Issue.4 , pp. 859-868
    • Lund, C.1    Fortnow, L.2    Karloff, H.3    Nisan, N.4
  • 164
    • 0000789645 scopus 로고
    • Explicit construction of concentrators
    • (in Russian). English translation in Problems of Infor. Trans., pages 325–332, 1975
    • G. A. Margulis. Explicit Construction of Concentrators. Prob. Per. Infor., Vol. 9 (4), pages 71–80, 1973 (in Russian). English translation in Problems of Infor. Trans., pages 325–332, 1975.
    • (1973) Prob. Per. Infor , vol.9 , Issue.4 , pp. 71-80
    • Margulis, G.A.1
  • 165
    • 0034854953 scopus 로고    scopus 로고
    • Computationally sound proofs
    • Preliminary version in 35th FOCS, 1994
    • S. Micali. Computationally Sound Proofs. SIAM Journal on Computing, Vol. 30 (4), pages 1253–1298, 2000. Preliminary version in 35th FOCS, 1994.
    • (2000) SIAM Journal on Computing , vol.30 , Issue.4 , pp. 1253-1298
    • Micali, S.1
  • 166
    • 0017217375 scopus 로고
    • Riemann’s hypothesis and tests for primality
    • G. L. Miller. Riemann’s Hypothesis and Tests for Primality. Journal of Computer and System Science, Vol. 13, pages 300–317, 1976.
    • (1976) Journal of Computer and System Science , vol.13 , pp. 300-317
    • Miller, G.L.1
  • 167
    • 29144500344 scopus 로고    scopus 로고
    • Derandomizing arthur-merlin games using hitting sets
    • Preliminary version in 40th FOCS, 1999
    • P.B. Miltersen and N.V. Vinodchandran. Derandomizing Arthur-Merlin Games Using Hitting Sets. Computational Complexity, Vol. 14 (3), pages 256–279, 2005. Preliminary version in 40th FOCS, 1999.
    • (2005) Computational Complexity , vol.14 , Issue.3 , pp. 256-279
    • Miltersen, P.B.1    Vinodchandran, N.V.2
  • 169
    • 0001448484 scopus 로고
    • Bit commitment using pseudorandom generators
    • M. Naor. Bit Commitment Using Pseudorandom Generators. Journal of Cryptology, Vol. 4, pages 151–158, 1991.
    • (1991) Journal of Cryptology , vol.4 , pp. 151-158
    • Naor, M.1
  • 170
    • 0027641832 scopus 로고
    • Small-bias probability spaces: Efficient constructions and applications
    • Preliminary version in 22nd STOC, 1990
    • J. Naor and M. Naor. Small-Bias Probability Spaces: Efficient Constructions and Applications. SIAM Journal on Computing, Vol. 22, pages 838–856, 1993. Preliminary version in 22nd STOC, 1990.
    • (1993) SIAM Journal on Computing , vol.22 , pp. 838-856
    • Naor, J.1    Naor, M.2
  • 171
    • 0024867751 scopus 로고
    • Universal one-way hash functions and their cryptographic application
    • M. Naor and M. Yung. Universal One-Way Hash Functions and Their Cryptographic Application. In 21st ACM Symposium on the Theory of Computing, pages 33–43, 1989.
    • (1989) 21St ACM Symposium on the Theory of Computing , pp. 33-43
    • Naor, M.1    Yung, M.2
  • 173
    • 0008827213 scopus 로고
    • Pseudorandom bits for constant depth circuits
    • N. Nisan. Pseudorandom Bits for Constant Depth Circuits. Combinatorica, Vol. 11 (1), pages 63–70, 1991.
    • (1991) Combinatorica , vol.11 , Issue.1 , pp. 63-70
    • Nisan, N.1
  • 174
    • 0000947929 scopus 로고
    • Pseudorandom generators for space bounded computation
    • Preliminary version in 22nd STOC, 1990
    • N. Nisan. Pseudorandom Generators for Space Bounded Computation. Combinatorica, Vol. 12 (4), pages 449–461, 1992. Preliminary version in 22nd STOC, 1990.
    • (1992) Combinatorica , vol.12 , Issue.4 , pp. 449-461
    • Nisan, N.1
  • 175
    • 0038874554 scopus 로고
    • Rl ? Sc
    • Preliminary version in 24th STOC, 1992
    • N. Nisan. RL ? SC. Computational Complexity, Vol. 4, pages 1-11, 1994. Preliminary version in 24th STOC, 1992.
    • (1994) Computational Complexity , vol.4 , pp. 1-11
    • Nisan, N.1
  • 176
    • 0028516244 scopus 로고
    • Hardness vs randomness
    • Preliminary version in 29th FOCS, 1988
    • N. Nisan and A. Wigderson. Hardness vs Randomness. Journal of Computer and System Science, Vol. 49 (2), pages 149–167, 1994. Preliminary version in 29th FOCS, 1988.
    • (1994) Journal of Computer and System Science , vol.49 , Issue.2 , pp. 149-167
    • Nisan, N.1    Wigderson, A.2
  • 177
    • 0030086632 scopus 로고    scopus 로고
    • Randomness is linear in space
    • Preliminary version in 25th STOC, 1993
    • N. Nisan and D. Zuckerman. Randomness Is Linear in Space. Journal of Computer and System Science, Vol. 52 (1), pages 43–52, 1996. Preliminary version in 25th STOC, 1993.
    • (1996) Journal of Computer and System Science , vol.52 , Issue.1 , pp. 43-52
    • Nisan, N.1    Zuckerman, D.2
  • 180
    • 0018456413 scopus 로고
    • Relations among complexity measures
    • N. Pippenger and M. J. Fischer. Relations Among Complexity Measures. Journal of the ACM, Vol. 26 (2), pages 361–381, 1979.
    • (1979) Journal of the ACM , vol.26 , Issue.2 , pp. 361-381
    • Pippenger, N.1    Fischer, M.J.2
  • 181
    • 84966244301 scopus 로고
    • A variant of a recursively unsolvable problem
    • E. Post. A Variant of a Recursively Unsolvable Problem. Bull. AMS, Vol. 52, pages 264–268, 1946.
    • (1946) Bull. AMS , vol.52 , pp. 264-268
    • Post, E.1
  • 182
    • 0010277907 scopus 로고
    • Digitalized signatures
    • (R. A. DeMillo et al. eds.), Academic Press
    • M. O. Rabin. Digitalized Signatures. In Foundations of Secure Computation (R. A. DeMillo et al. eds.), Academic Press, 1977.
    • (1977) Foundations of Secure Computation
    • Rabin, M.O.1
  • 184
    • 33845432604 scopus 로고
    • Probabilistic algorithm for testing primality
    • M. O. Rabin. Probabilistic Algorithm for Testing Primality. Journal of Number Theory, Vol. 12, pages 128–138, 1980.
    • (1980) Journal of Number Theory , vol.12 , pp. 128-138
    • Rabin, M.O.1
  • 185
    • 0001226672 scopus 로고    scopus 로고
    • A parallel repetition theorem
    • Extended abstract in 27th STOC, 1995
    • R. Raz. A Parallel Repetition Theorem. SIAM Journal on Computing, Vol. 27 (3), pages 763–803, 1998. Extended abstract in 27th STOC, 1995.
    • (1998) SIAM Journal on Computing , vol.27 , Issue.3 , pp. 763-803
    • Raz, R.1
  • 186
    • 0026888974 scopus 로고
    • Monotone circuits for matching require linear depth
    • Preliminary version in 22nd STOC, 1990
    • R. Raz and A. Wigderson. Monotone Circuits for Matching Require Linear Depth. Journal of the ACM, Vol. 39 (3), pages 736–744, 1992. Preliminary version in 22nd STOC, 1990.
    • (1992) Journal of the ACM , vol.39 , Issue.3 , pp. 736-744
    • Raz, R.1    Wigderson, A.2
  • 187
    • 0000574714 scopus 로고
    • Lower bounds for the monotone complexity of some boolean functions
    • (in Russian). English translation in Soviet Math. Doklady, Vol. 31, pages 354–357, 1985
    • A. Razborov. Lower Bounds for the Monotone Complexity of some Boolean Functions. In Doklady Akademii Nauk SSSR, Vol. 281 (4), pages 798–801, 1985 (in Russian). English translation in Soviet Math. Doklady, Vol. 31, pages 354–357, 1985.
    • (1985) Doklady Akademii Nauk SSSR , vol.281 , Issue.4 , pp. 798-801
    • Razborov, A.1
  • 188
    • 0000883554 scopus 로고    scopus 로고
    • Lower bounds on the size of bounded-depth networks over a complete basis with logical addition
    • 1987 (in Russian). English translation in Mathematical Notes of the Academy of Sci. of the USSR, Vol. 41 (4), pages 333–338, 1987
    • A. Razborov. Lower Bounds on the Size of Bounded-Depth Networks over a Complete Basis with Logical Addition. In Matematicheskie Zametki, Vol. 41 (4), pages 598–607, 1987 (in Russian). English translation in Mathematical Notes of the Academy of Sci. of the USSR, Vol. 41 (4), pages 333–338, 1987.
    • Matematicheskie Zametki , vol.41 , Issue.4 , pp. 598-607
    • Razborov, A.1
  • 189
    • 0031213341 scopus 로고    scopus 로고
    • Natural proofs
    • Preliminary version in 26th STOC, 1994
    • A. R. Razborov and S. Rudich. Natural Proofs. Journal of Computer and System Science, Vol. 55 (1), pages 24–35, 1997. Preliminary version in 26th STOC, 1994.
    • (1997) Journal of Computer and System Science , vol.55 , Issue.1 , pp. 24-35
    • Razborov, A.R.1    Rudich, S.2
  • 191
    • 0036000527 scopus 로고    scopus 로고
    • Entropy waves, the zig-zag graph product, and new constant-degree expanders and extractors
    • Preliminary version in 41st FOCS, pages 3–13, 2000
    • O. Reingold, S. Vadhan, and A. Wigderson. Entropy Waves, the Zig-Zag Graph Product, and New Constant-Degree Expanders and Extractors. Annals of Mathematics, Vol. 155 (1), pages 157–187, 2001. Preliminary version in 41st FOCS, pages 3–13, 2000.
    • (2001) Annals of Mathematics , vol.155 , Issue.1 , pp. 157-187
    • Reingold, O.1    Vadhan, S.2    Wigderson, A.3
  • 192
    • 0001125131 scopus 로고
    • Classes of recursively enumerable sets and their decision problems
    • H. G. Rice. Classes of Recursively Enumerable Sets and Their Decision Problems. Trans. AMS, Vol. 89, pages 25–59, 1953.
    • (1953) Trans. AMS , vol.89 , pp. 25-59
    • Rice, H.G.1
  • 193
    • 0017930809 scopus 로고
    • A method for obtaining digital signatures and public key cryptosystems
    • (Feb.)
    • R. L. Rivest, A. Shamir, and L.M. Adleman. A Method for Obtaining Digital Signatures and Public Key Cryptosystems. CACM, Vol. 21 (Feb.), pages 120–126, 1978.
    • (1978) CACM , vol.21 , pp. 120-126
    • Rivest, R.L.1    Shamir, A.2    Adleman, L.M.3
  • 194
    • 0013370155 scopus 로고    scopus 로고
    • Property testing
    • S. Rajasekaran, P. M. Pardalos, J. H. Reif, and J. D. P. Rolim (eds
    • D. Ron. Property Testing. In Handbook on Randomization, Volume 2, S. Rajasekaran, P. M. Pardalos, J. H. Reif, and J. D. P. Rolim (eds.), pages 597–649, 2001.
    • (2001) Handbook on Randomization , vol.2 , pp. 597-649
    • Ron, D.1
  • 195
    • 0030128622 scopus 로고    scopus 로고
    • Robust characterization of polynomials with applications to program testing
    • R. Rubinfeld and M. Sudan. Robust Characterization of Polynomials with Applications to Program Testing. SIAM Journal on Computing, Vol. 25 (2), pages 252–271, 1996.
    • (1996) SIAM Journal on Computing , vol.25 , Issue.2 , pp. 252-271
    • Rubinfeld, R.1    Sudan, M.2
  • 196
    • 0032621057 scopus 로고    scopus 로고
    • Bphspace(s) ? Dspace(s3/2)
    • Preliminary version in 36th FOCS, 1995
    • M. Saks and S. Zhou. BPHSPACE(S) ? DSPACE(S3/2). Journal of Computer and System Science, Vol. 58 (2), pages 376–403, 1999. Preliminary version in 36th FOCS, 1995.
    • (1999) Journal of Computer and System Science , vol.58 , Issue.2 , pp. 376-403
    • Saks, M.1    Zhou, S.2
  • 197
    • 0014776888 scopus 로고
    • Relationships between nondeterministic anddeterministic tape complexities
    • W. J. Savitch. Relationships Between Nondeterministic andDeterministic Tape Complexities. Journal of Computer and System Science, Vol. 4 (2), pages 177–192, 1970.
    • (1970) Journal of Computer and System Science , vol.4 , Issue.2 , pp. 177-192
    • Savitch, W.J.1
  • 198
    • 37149011064 scopus 로고
    • On the structure of np
    • A. Selman. On the Structure of NP. Notices Amer. Math. Soc., Vol. 21 (6), page 310, 1974.
    • (1974) Notices Amer. Math. Soc , vol.21 , Issue.6 , pp. 310
    • Selman, A.1
  • 199
    • 84976779342 scopus 로고
    • Fast probabilistic algorithms for verification of polynomial identities
    • October
    • J. T. Schwartz. Fast Probabilistic Algorithms for Verification of Polynomial Identities. Journal of the ACM, Vol. 27 (4), pages 701–717, October 1980.
    • (1980) Journal of the ACM , vol.27 , Issue.4 , pp. 701-717
    • Schwartz, J.T.1
  • 200
    • 0012579059 scopus 로고    scopus 로고
    • Recent developments in explicit constructions of extractors
    • : Algorithms and Complexity, G. Paun, G. Rozenberg, and A. Salomaa (eds.), World Scientific, 2004. Preliminary version in Bulletin of the EATCS 77
    • R. Shaltiel. Recent Developments in Explicit Constructions of Extractors. In Current Trends in Theoretical Computer Science: The Challenge of the New Century, Vol. 1: Algorithms and Complexity, G. Paun, G. Rozenberg, and A. Salomaa (eds.), World Scientific, 2004. Preliminary version in Bulletin of the EATCS 77, pages 67–95, 2002.
    • (2002) Current Trends in Theoretical Computer Science: The Challenge of the New Century , vol.1 , pp. 67-95
    • Shaltiel, R.1
  • 202
    • 0026930543 scopus 로고
    • Ip = pspace
    • Preliminary version in 31st FOCS, 1990
    • A. Shamir. IP = PSPACE. Journal of the ACM, Vol. 39 (4), pages 869–877, 1992. Preliminary version in 31st FOCS, 1990.
    • (1992) Journal of the ACM , vol.39 , Issue.4 , pp. 869-877
    • Shamir, A.1
  • 204
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • C. E. Shannon. A Mathematical Theory of Communication. Bell Sys. Tech. Jour., Vol. 27, pages 623–656, 1948.
    • (1948) Bell Sys. Tech. Jour , vol.27 , pp. 623-656
    • Shannon, C.E.1
  • 205
    • 84890522850 scopus 로고
    • Communication theory of secrecy systems
    • C. E. Shannon. Communication Theory of Secrecy Systems. Bell Sys. Tech. Jour., Vol. 28, pages 656–715, 1949.
    • (1949) Bell Sys. Tech. Jour , vol.28 , pp. 656-715
    • Shannon, C.E.1
  • 206
    • 0345015878 scopus 로고    scopus 로고
    • Lower bounds for matrix product
    • A. Shpilka. Lower Bounds for Matrix Product. SIAM Journal on Computing, pages 1185-1200, 2003.
    • (2003) SIAM Journal on Computing , pp. 1185-1200
    • Shpilka, A.1
  • 209
    • 0023570259 scopus 로고
    • Algebraic methods in the theory of lower bounds for boolean circuit complexity
    • R. Smolensky. Algebraic Methods in the Theory of Lower Bounds for Boolean Circuit Complexity. In 19th ACM Symposium on the Theory of Computing, pages 77–82, 1987.
    • (1987) 19Th ACM Symposium on the Theory of Computing , pp. 77-82
    • Smolensky, R.1
  • 210
    • 4544279425 scopus 로고
    • A formal theory of inductive inference
    • R. J. Solomonoff. A Formal Theory of Inductive Inference. Information and Control, Vol. 7 (1), pages 1–22, 1964.
    • (1964) Information and Control , vol.7 , Issue.1 , pp. 1-22
    • Solomonoff, R.J.1
  • 211
    • 0001873077 scopus 로고
    • A fast monte-carlo test for primality
    • Addendum in SIAM Journal on Computing, Vol. 7, page 118, 1978
    • R. Solovay and V. Strassen. A Fast Monte-Carlo Test for Primality. SIAM Journal on Computing, Vol. 6, pages 84–85, 1977. Addendum in SIAM Journal on Computing, Vol. 7, page 118, 1978.
    • (1977) SIAM Journal on Computing , vol.6 , pp. 84-85
    • Solovay, R.1    Strassen, V.2
  • 212
    • 85032415439 scopus 로고    scopus 로고
    • Lectures 10 and 11. Notes (by D. Lewin and S. Vadhan), March
    • D. A. Spielman. Advanced Complexity Theory, Lectures 10 and 11. Notes (by D. Lewin and S. Vadhan), March 1997. Available from http://www.cs.yale.edu/homes/spielman/AdvComplexity/1998/aslect10.ps and lect11.ps.
    • (1997) Advanced Complexity Theory
    • Spielman, D.A.1
  • 216
    • 0031097176 scopus 로고    scopus 로고
    • Decoding of reed solomon codes beyond the error-correction bound
    • M. Sudan. Decoding of Reed Solomon Codes Beyond the Error-Correction Bound. Journal of Complexity, Vol. 13 (1), pages 180–193, 1997.
    • (1997) Journal of Complexity , vol.13 , Issue.1 , pp. 180-193
    • Sudan, M.1
  • 217
    • 26944481662 scopus 로고    scopus 로고
    • Algorithmic introduction to coding theory
    • M. Sudan. Algorithmic Introduction to Coding Theory. Lecture notes, available from http://theory.csail.mit.edu/˜madhu/FT01/, 2001.
    • Lecture Notes
    • Sudan, M.1
  • 219
    • 0024112189 scopus 로고
    • A method of forced enumeration for nondeterministic automata
    • R. Szelepcsenyi. A Method of Forced Enumeration for Nondeterministic Automata. Acta Informatica, Vol. 26, pages 279–284, 1988.
    • (1988) Acta Informatica , vol.26 , pp. 279-284
    • Szelepcsenyi, R.1
  • 220
    • 0026239342 scopus 로고
    • Pp is as hard as the polynomial-time hierarchy
    • S. Toda. PP Is as Hard as the Polynomial-Time Hierarchy. SIAM Journal on Computing, Vol. 20 (5), pages 865–877, 1991.
    • (1991) SIAM Journal on Computing , vol.20 , Issue.5 , pp. 865-877
    • Toda, S.1
  • 221
    • 78951485210 scopus 로고
    • A survey of russian approaches to perebor (brute force search) algorithms
    • B. A. Trakhtenbrot. A Survey of Russian Approaches to Perebor (Brute Force Search) Algorithms. Annals of the History of Computing, Vol. 6 (4), pages 384–398, 1984.
    • (1984) Annals of the History of Computing , vol.6 , Issue.4 , pp. 384-398
    • Trakhtenbrot, B.A.1
  • 222
    • 0005314594 scopus 로고    scopus 로고
    • Extractors and pseudorandom generators
    • Preliminary version in 31st STOC, 1999
    • L. Trevisan. Extractors and Pseudorandom Generators. Journal of the ACM, Vol. 48 (4), pages 860–879, 2001. Preliminary version in 31st STOC, 1999.
    • (2001) Journal of the ACM , vol.48 , Issue.4 , pp. 860-879
    • Trevisan, L.1
  • 224
    • 34848840337 scopus 로고    scopus 로고
    • An o(log n log log n) space algorithm for undirected st-connectivity
    • V. Trifonov. An O(log n log log n) Space Algorithm for Undirected st-Connectivity. In 37th ACM Symposium on the Theory of Computing, pages 623–633, 2005.
    • (2005) 37Th ACM Symposium on the Theory of Computing , pp. 623-633
    • Trifonov, V.1
  • 225
    • 84960561455 scopus 로고
    • On computable numbers, with an application to the entscheidungsproblem
    • A Correction, ibid., Vol. 43, pages 544–546
    • A. M. Turing. On Computable Numbers, with an Application to the Entscheidungsproblem. Proc. Londom Mathematical Soceity, Ser. 2, Vol. 42, pages 230–265, 1936. A Correction, Vol. 43, pages 544–546.
    • (1936) Proc. Londom Mathematical Soceity , vol.42 , pp. 230-265
    • Turing, A.M.1
  • 226
    • 0142027847 scopus 로고    scopus 로고
    • Pseudo-random generators for all hardness
    • C. Umans. Pseudo-Random Generators for All Hardness. Journal of Computer and System Science, Vol. 67 (2), pages 419–440, 2003.
    • (2003) Journal of Computer and System Science , vol.67 , Issue.2 , pp. 419-440
    • Umans, C.1
  • 228
    • 34547839124 scopus 로고    scopus 로고
    • An unconditional study of computational zero knowledge
    • Extended abstract in 45th FOCS, 2004
    • S. Vadhan. An Unconditional Study of Computational Zero Knowledge. SIAM Journal on Computing, Vol. 36 (4), pages 1160–1214, 2006. Extended abstract in 45th FOCS, 2004.
    • (2006) SIAM Journal on Computing , vol.36 , Issue.4 , pp. 1160-1214
    • Vadhan, S.1
  • 230
    • 49249151236 scopus 로고
    • The complexity of computing the permanent
    • L. G. Valiant. The Complexity of Computing the Permanent. Theoretical Computer Science, Vol. 8, pages 189–201, 1979.
    • (1979) Theoretical Computer Science , vol.8 , pp. 189-201
    • Valiant, L.G.1
  • 232
    • 0021518106 scopus 로고
    • A theory of the learnable
    • L. G. Valiant. A Theory of the Learnable. CACM, Vol. 27 (11), pages 1134–1142, 1984.
    • (1984) CACM , vol.27 , Issue.11 , pp. 1134-1142
    • Valiant, L.G.1
  • 233
    • 0022911518 scopus 로고
    • Np is as easy as detecting unique solutions
    • L. G. Valiant and V. V. Vazirani. NP Is as Easy as Detecting Unique Solutions. Theoretical Computer Science, Vol. 47 (1), pages 85–93, 1986.
    • (1986) Theoretical Computer Science , vol.47 , Issue.1 , pp. 85-93
    • Valiant, L.G.1    Vazirani, V.V.2
  • 234
    • 0004014994 scopus 로고
    • Contract No. W-670-ORD- 492, Moore School of Electrical Engineering, Univ. of Pennsylvania. Reprinted (in part) in Origins of Digital Computers: Selected Papers, Springer-Verlag
    • J. von Neumann. First Draft of a Report on the EDVAC, 1945. Contract No. W-670-ORD- 492, Moore School of Electrical Engineering, Univ. of Pennsylvania. Reprinted (in part) in Origins of Digital Computers: Selected Papers, Springer-Verlag, pages 383–392, 1982.
    • (1945) First Draft of a Report on the EDVAC , pp. 383-392
    • Von Neumann, J.1
  • 235
    • 21244466146 scopus 로고
    • Zur theorie der gesellschaftsspiele
    • J. von Neumann, Zur Theorie der Gesellschaftsspiele. Mathematische Annalen, 100, pages 295–320, 1928.
    • (1928) Mathematische Annalen , vol.100 , pp. 295-320
    • Von Neumann, J.1
  • 242
    • 40549114927 scopus 로고    scopus 로고
    • Towards 3-query locally decodable codes of subexponential length
    • S. Yekhanin. Towards 3-Query Locally Decodable Codes of Subexponential Length. In 39th ACM Symposium on the Theory of Computing, pages 266–274, 2007.
    • (2007) 39Th ACM Symposium on the Theory of Computing , pp. 266-274
    • Yekhanin, S.1
  • 244
    • 33748109880 scopus 로고    scopus 로고
    • Linear-degree extractors and the inapproximability of max-clique and chromatic number
    • D. Zuckerman. Linear-Degree Extractors and the Inapproximability of Max-Clique and Chromatic Number. In 38th ACM Symposium on the Theory of Computing, pages 681–690, 2006.
    • (2006) 38Th ACM Symposium on the Theory of Computing , pp. 681-690
    • Zuckerman, D.1


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