Polylogarithmic-round interactive proofs for coNP collapse the exponential hierarchy

Theoretical Computer Science

Volumn 385, Issue 1-3, 2007, Pages 167-178

  Pavan, A ^a   Selman, Alan L ^b   Sengupta, Samik ^b   Vinodchandran, N V ^c  

^a Iowa State University   (United States)

^b State University of New York   (United States)

^c UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

Complexity classes; Interactive proof systems; Non uniform complexity

Indexed keywords

FORMAL LANGUAGES; INTERACTIVE COMPUTER SYSTEMS; PROBLEM SOLVING; THEOREM PROVING;

COMPLEXITY CLASSES; INTERACTIVE PROOF SYSTEMS; NON-UNIFORM COMPLEXITY;

ASYMPTOTIC STABILITY;

EID: 34548701346     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2007.06.013     Document Type: Article

References (28)

1. Arvind V., Köbler J., Schöning U., and Schuler R. If NP has polynomial-size circuits, then MA = AM. Theoretical Computer Science 137 2 (1995) 279-282
2. Arora S., Lund C., Motwani R., Sudan M., and Szegedy M. Proof verification and hardness of approximation problems. Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science (1992), IEEE Computer Society Press 14-22
3. Arora S., and Safra S. Approximating clique is NP-complete. Proceedings of the 33rd Annual IEEE Symposium on Foundations on Computer Science (1992), IEEE Computer Society Press 2-13
4. Babai L. Trading group theory for randomness. Proceedings of the 17th Symposium on Theory of Computing (1985), ACM Press 421-429
5. Balcázar J.L., Díaz J., and Gabarró J. Structural Complexity II. EATCS Monographs on Theoretical Computer Science (1990), Springer-Verlag, Berlin, Heidelberg
6. Balcázar J.L., Díaz J., and Gabarró J. Structural Complexity I. 2nd edition. EATCS Monographs on Theoretical Computer Science (1995), Springer-Verlag, Berlin, Heidelberg
7. Babai L., Fortnow L., and Lund C. Nondeterministic exponential time has two-prover interactive protocols. Computational Complexity 1 1 (1981) 3-40
8. L. Babai, L. Fortnow, L. Levin, M. Szegedy, Checking computations in polylogarithmic time, in: Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, 1991, pp. 21-31
9. Buhrman H., and Homer S. Superpolynomial circuits, almost sparse oracles, and the exponential hierarchy. Foundations of Software Technology and Theoretical Computer Science. 12th Conference, New Delhi, India, 18-20 December 1992, Proceedings. Lecture Notes in Computer Science vol. 652 (1992), Springer-Verlag 116-127
10. Boppana R.B., Håstad J., and Zachos S. Does co-NP have short interactive proofs?. Information Processing Letters 25 2 (1987) 127-132
11. Babai L., and Moran S. Arthur-Merlin games: A randomized proof system, and a hierarchy of complexity classes. Journal of Computer and System Sciences 36 (1988) 254-276
12. M. Ben-Or, S. Goldwasser, J. Kilian, A. Wigderson, Multiprover interactive proofs: How to remove the intractability assumptions, in: Proceedings of the 20th Annual ACM Symposium on Theory of Computing, 1988, pp. 113-131
13. NP, in: Proceedings of the 42nd IEEE Conference on Foundations of Computer Science, 2001, pp. 620-629
14. Canetti R. On BPP and the polynomial-time hierarchy. Information Processing Letters (1996) 237-241
15. J.-Y. Cai, V. Chakaravarthy, L. Hemaspaandra, M. Ogihara, Competing provers yield improved Karp-Lipton collapse results, in: Proceedings 20th Symposium on Theoretical Aspects of Computer Science, 2003, pp. 535-546
16. Feige U., Goldwasser S., Lovász L., Safra S., and Szegedy M. Approximating clique is almost NP-complete. Proceedings 32nd Symposium on Foundations of Computer Science (1991), IEEE Computer Society Press 2-12
17. S. Goldwasser, S. Micali, C. Rackoff, The knowledge complexity of interactive proofs, in: Proceedings of the 17th Annual ACM Symposium on Theory of Computing, 1985, pp. 291-304
18. Goldwasser S., and Sipser M. Private coins versus public coins in interactive proof systems. In: Micali S. (Ed). Randomness and Computation. Advances in Computing Research vol. 5 (1989), JAI Press 73-90
19. Goldreich O., Vadhan S., and Wigderson A. On interactive proofs with laconic provers. Proceedings of the 28th International Colloquium on Automata, Languages, and Programming. Lecture Notes in Computer Science vol. 2076 (2001), Springer-Verlag 334-345
20. Homer S., and Selman A. Computability and Complexity Theory (2001), Springer-Verlag
21. R. Karp, R. Lipton, Some connections between nonuniform and uniform complexity classes, in: Proceedings of the 12th ACM Symposium on Theory of Computing, 1980, pp. 302-309
22. Lund C., Fortnow L., Karloff H., and Nisan N. Algebraic methods for interactive proof systems. Journal of the Association for Computing Machinery 39 4 (1992) 859-868
23. Russell A., and Sundaram R. Symmetric alternation captures BPP. Journal of Computational Complexity 7 2 (1998) 152-162
24. Shamir A. IP = PSPACE. Journal of the Association for Computing Machinery 39 4 (1992) 869-877
25. Toda S. PP is as hard as the polynomial time hierarchy. SIAM Journal on Computing 20 (1991) 865-877
26. Yap C. Some consequences of non-uniform conditions on uniform classes. Theoretical Computer Science 26 3 (1983) 287-300
27. Zachos S., and Fürer M. Probabilistic quantifiers vs distrustful adversaries. Foundations of Software Technology and Theoretical Computer Science, 1987, Proceedings. Lecture Notes in Computer Science vol. 287 (1987), Springer-Verlag 449-455
28. Zachos S., and Heller H. A decisive characterization of BPP. Information and Control 69 (1986) 125-135