Algebrization: A new barrier in complexity theory

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2008, Pages 731-740

  Aaronson, Scott ^a   Wigderson, Avi ^b  

^a MIT MEDIA LAB   (United States)

^b INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

Theory

Indexed keywords

ALGEBRAIC QUERIES; BASIC RESULTS; CIRCUIT LOWER BOUNDS; COMMUNICATION COMPLEXITIES; COMPLEXITY CLASSES; COMPLEXITY THEORIES; FINITE FIELDS; INNER PRODUCTS; LOWER BOUNDS; NEW MODELS; OPEN PROBLEMS; SUPERLINEAR; THEORY;

COMPUTATIONAL COMPLEXITY; COMPUTER NETWORKS; INCLUSIONS; INTERNET PROTOCOLS; NETWORKS (CIRCUITS); PLASMA WAVES;

CONTROL THEORY;

EID: 57049109378     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (31)

1. S. Aaronson. Oracles are subtle but not malicious. In Proc. IEEE Complexity, p. 340-354, 2006.
2. S. Arora, R. Impagliazzo, and U. Vazirani. Relativizing versus nonrelativizing techniques: the role of local checkability. Manuscript, 1992.
3. L. Babai, L. Fortnow, and C. Lund. Nondeterministic exponential time has two-prover interactive protocols. Computational Complexity, 1(1):3-40, 1991.
4. T. Baker, J. Gill, and R. Solovay. Relativizations of the P=?NP question. SIAM J. Comput., 4:431-442, 1975.
5. H. Buhrman, L. Fortnow, and T. Thierauf. Nonrelativizing separations. In Proc. IEEE Complexity, p. 8-12, 1998.
6. H. Buhrman, N. Vereshchagin, and R. de Wolf. On computation and communication with small bias. In Proc. IEEE Complexity, p. 24-32, 2007.
7. H. Buhrman and R. de Wolf. Complexity measures and decision tree complexity: a survey. Theoretical Comput. Set., 288:21-43, 2002.
8. A. K. Chandra, D. Kozen, and L. J. Stockmeyer. Alternation. J. ACM, 28(1):114-133, 1981.
9. L. Fortnow. The role of relativization in complexity theory. Bulletin of the EATCS, 52:229-244, February 1994.
10. O. Goldreich, S. Micali, and A. Wigderson. Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems. J. ACM, 38(1):691-729, 1991.
11. J. Hartmanis, R. Chang, S. Chari, D. Ranjan, and P. Rohatgi. Relativization: a revisionistic perspective. Bulletin of the EATCS, 47:144-153, 1992.
12. J. Hartmanis and R.. E. Stearns. On the computational complexity of algorithms. Transactio7is of the American Mathematical Society, 117:285-306, 1965.
13. J. E. Hopcroft, W. J. Paul, and L. G. Valiant. On time versus space. J. ACM, 24(2):332-337, 1977.
14. A. Juma, V. Kabanets, C. Rackoff, and A. Shpilka. The black-box query complexity of polynomial summation. ECCC TR07-125, 2007.
15. B. Kalyanasundaram and G. Schnitger. The probabilistic communication complexity of set intersection. SIAM J. Discrete Math, 5(4):545-557, 1992.
16. R. Kannan. Circuit-size lower bounds and non-reducibility to sparse sets. Information and Control, 55:40-56, 1982.
17. H. Klauck. Rectangle size bounds and threshold covers in communication complexity. In Proc. IEEE Complexity, p. 118-134, 2003.
18. A. Klivans and D. van Melkebeek. Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses. SIAM J. Comput., 31:1501-1526, 2002.
19. C. Lund, L. Fortnow, H. Karloff, and N. Nisan. Algebraic methods for interactive proof systems. J. ACM, 39:859-868, 1992.
20. R. Raz. Exponential separation of quantum and classical communication complexity. In Proc. ACM STOC, p. 358-367, 1999.
21. R. Raz and A. Shpilka. On the power of quantum proofs. In Proc. IEEE Complexity, p. 260-274, 2004.
22. A. A. Razborov. Lower bounds for the size of circuits of bounded depth with basis {&, ⊕}. Mathematicheskie Zametki, 41(4):598-607, 1987.
23. A. A. Razborov. On the distributional complexity of disjointness. Theoretical Comput. Sci., 106:385-390, 1992.
24. A. A. Razborov. Quantum communication complexity of symmetric predicates. Izvestiya Math., 67(1):145-159, 2003.
25. A. A. R.azborov and S. Rudich. Natural proofs. J. Comput. Sys. Set., 55(l):24-35, 1997.
26. R. Santhanam. Circuit lower bounds for Merlin-Arthur classes. In Proc. ACM STOC, p. 275-283, 2007.
27. A. Shamir. 1P=PSPACE. J. ACM, 39(4):869-877, 1992.
28. S. Toda. PP is as hard as the polynomial-time hierarchy. SIAM J. Comput, 20(5):865-877, 1991.
29. N. V. Vinodchandran. A note on the circuit complexity of PP. ECCC TR04-056, 2004.
30. C. B. Wilson. Relativized circuit complexity. J. Comput. Sys. Sci., 31(2):169-181, 1985.
31. A. C-C. Yao. How to generate and exchange secrets (extended abstract). In Proc. IEEE FOCS, p. 162-167, 1986.