Pseudorandomness for approximate counting and sampling

Computational Complexity

Volumn 15, Issue 4, 2006, Pages 298-341

  Shaltiel, Ronen ^a   Umans, Christopher ^b  

^a UNIVERSITY OF HAIFA   (Israel)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Approximate counting; Arthur Merlin games; Derandomization; Nondeterministic circuits; Pseudorandomness

Indexed keywords

EID: 34249055556     PISSN: 10163328     EISSN: 14208954     Source Type: Journal    
DOI: 10.1007/s00037-007-0218-9     Document Type: Conference Paper

References (34)

1. E. ALLENDER, M. KOUCKY, D. RONNEBURGER & S. ROY (2003). Derandomization and Distinguishing Complexity. In Proceedings of the 18th Annual IEEE Conference on Computational Complexity, 209-220.
2. V. ARVIND & J. KÖBLER (2001). On Pseudorandomness and Resource-bounded Measure. Theoretical Computer Science 255.
3. L. BABAI (1985). Trading group theory for randomness. In Proceedings of the Seventeenth Annual ACM Symposium on Theory of Computing.
4. L. BABAI, L. FORTNOW, N. NISAN & A. WIGDERSON (1993). BPP Has Subexponential Time Simulations Unless EXPTIME has Publishable Proofs. Computational Complexity 3(4), 307-318.
5. D. BEAVER & J. FEIGENBAUM (1990). Hiding Instances in Multioracle Queries. In 7th Annual Symposium on Theoretical Aspects of Computer Science, volume 415 of LNCS, 37-48. Springer.
6. M. BELLARE, O. GOLDREICH & E. PETRANK (2000). Uniform Generation of NP-Witnesses Using an NP-Oracle. Information and Computation (formerly Information and Control) 163.
7. M. BELLARE & J. ROMPEL (1994). Randomness-efficient oblivious sampling. In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, SHAFI GOLDWASSER, editor, 276-287.
8. S. BEN-DAVID, B. CHOR, O. GOLDREICH & M. LUBY (1990). On the theory of average case complexity. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, 379-386.
9. M. BLUM & S. MICALI (1984). How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits. SIAM Journal on Computing 13(4), 850-864.
10. N. H. BSHOUTY, R. CLEVE, R. GAVALDA, S. KANNAN & C. TAMON (1996). Oracles and queries that are sufficient for exact learning. Journal of Computer and System Sciences 52(3), 421-433.
11. NP. In Proceedings of the 42nd Annual Symposium on Foundations of Computer Science, 620-629.
12. R. CANETTI (1996). On BPP and the Polynomial-Time Hierarchy. Information Processing Letters 57, 237-241.
13. J. FEIGENBAUM & L. FORTNOW (1993). Random-Self-Reducibility of Complete Sets. SIAM J. Comput. 22(5), 994-1005.
14. L. FORTNOW & A. KLIVANS (2005). NP with Small Advice. In Proceedings of the 20th Annual IEEE Conference on Computational Complexity, 228-234.
15. O. GOLDREICH (1997). A Sample of Samplers - A Computational Perspective on Sampling (survey). In Electronic Colloquium on Computational Complexity, technical report TR 97-020.
16. O. GOLDREICH (1998). Modern Cryptography, Probabilistic Proofs and Pseudorandomness. Springer-Verlag, Algorithms and Combinatorics.
17. S. GOLDWASSER, S. MICALI & C. RACKOFF (1989). The knowledge complexity of interactive proof systems. SIAM Journal of Computing 18(1), 186-208.
18. Y. HAN, L. A. HEMASPAANDRA & T. THIERAUF (1997). Threshold Computation and Cryptographic Security. SIAM J. Comput. 26(1), 59-78.
19. R. IMPAGLIAZZO (1995). Hard-core distributions for somewhat hard problems. In 36th Annual Symposium on Foundations of Computer Science, 538-545.
20. R. IMPAGLIAZZO, R. SHALTIEL & A. WIGDERSON (1999). Near-optimal conversion of hardness into pseudo-randomness. In 40th Annual Symposium on Foundations of Computer Science, 181-190.
21. R. IMPAGLIAZZO, R. SHALTIEL &, A. WIGDERSON (2000). Extractors and pseudo-random generators with optimal seed length. In Proceedings of the thirty second annual Symposium on Theory of Computing, 1-10.
22. R. IMPAGLIAZZO & A. WIGDERSON (1997). P = BPP if E Requires Exponential Circuits: Derandomizing the XOR Lemma. In Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, 220-229.
23. M. R. JERRUM, L. G. VALIANT & V. V. VAZIRANI (1986). Random generation of combinatorial structures from a uniform distribution. Theoretical Computer Science 43(2-3), 169-188.
24. V. KABANETS (2002). Derandomization: A Brief Overview. In Electronic Colloquium on Computational Complexity, technical report, TR 02-008.
25. A. R. KLIVANS & D. VAN MELKEBEEK (2002). Graph Nonisomorphism Has Subexponential Size Proofs Unless the Polynomial-Time Hierarchy Collapses. SIAM Journal on Computing 31(5), 1501-1526.
26. P. B. MILTERSEN & N. V. VINODCHANDRAN (1999). Derandomizing Arthur-Merlin games using hitting sets. In 40th Annual Symposium on Foundations of Computer Science, 71-80.
27. N. NISAN & A. WIGDERSON (1994). Hardness vs Randomness. Journal of Computer and System Sciences 49(2), 149-167.
28. A. RUSSELL & R. SUNDARAM (1998). Symmetric Alternation Captures BPP. Computational Complexity 7(2), 152-162.
29. R. SHALTIEL & C. UMANS (2001). Simple extractors for all min-entropies and a new pseudo-random generator. In Proceedings of the 42nd Symposium on Foundations of Computer Science, 648-657.
30. L. STOCKMEYER (1983). The complexity of approximate counting. In Proceedings of the fifteenth annual Symposium on Theory of Computing, 118-126.
31. M. SUDAN, L. TREVISAN & S. VADHAN (2001). Pseudorandom generators without the XOR Lemma. Journal of Computer and System Sciences 62, 236-266.
32. C. UMANS (2003). Pseudo-Random Generators for all Hardnesses. Journal of Computer and System Sciences 67, 419-440.
33. L. R. WELCH & E. R. BERLEKAMP (1986). Error correction for algebraic block codes. U.S. Patent No. 4,633,470, issued December 30.
34. A. C. YAO (1982). Theory and Applications of Trapdoor Functions. In Proceedings of the 23th Annual Symposium on Foundations of Computer Science, 80-91.