On the existence of hard sparse sets under weak reductions

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1046, Issue , 1996, Pages 307-318

  Cai, Jin Yi ^a   Naik, Ashish V ^b   Sivakumar, D ^a  

^a State University of New York   (United States)

^b THE UNIVERSITY OF CHICAGO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

LOGSPACE; NP-HARD; POLYNOMIAL-TIME REDUCTION; PROBABILISTIC TECHNIQUE; SPARSE SET; TRUTH TABLES; TWO WAYS;

POLYNOMIAL APPROXIMATION;

EID: 84948183117     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-60922-9_26     Document Type: Conference Paper

References (32)

1. [AGHP90] N. Alon, O. Goldreich, J. Hastad, and R. Peralta. Simple constructions of almost k-wise independent random variables. In Proc. 31st FOCS, pages 544-553, 1990.
2. [AKM92] V. Arvind, J. Köbler, and M. Mundhenk. On bounded truth-table, conjunctive, and randomized reductions to sparse sets. In Proc. 12th FST & TCS, Lecture Notes in Computer Science, Springer-Verlag, 1992.
3. [Ber77] L. Berman. Polynomial Reducibilities and Complete Sets. PhD thesis, Cornell University, 1977.
4. [BH77] L. Berman and H. Hartmanis. On isomorphisms and density of NP and other complete sets. SIAM Journal on Computing, 6:305-322, 1977.
5. [BvzGH82] A. Borodin, J. von zur Gathen, and J. Hopcroft. Fast parallel matrix and GCD computations. Information and Control, 52:241-256, 1982.
6. [Bus87] S. Buss. The Boolean formula value problem is in ALOGTIME. In Proc. 19th STOC, pages 123-131, 1987.
7. [BCGR92] S. Buss, S. Cook, A. Gupta, and V. Ramachandran. An optimal parallel algorithm for formula evaluation. SIAM Journal on Computing, 21:755-780, 1992.
8. [CS95a] J. Cai and D. Sivakumar. The resolution of a Hartmanis conjecture. In Proc. 36th FOCS, pages 362-373, 1995.
9. [CS95b] J. Cai and D. Sivakumar. Resolution of Hartmanis'Conjecture for NL-hard sparse sets. Submitted, 1995.
10. [Chi85] A.L. Chistov. Fast parallel calculation of the rank of matrices over a field of arbitrary characteristic. In Proc. 5th FCT, Lecture Notes in Computer Science, pages 63-69. Springer-Verlag, 1985.
11. [Coo85] S. Cook. A taxonomy of problems with fast parallel algorithms. Information and Control, 64:2-22, 1985.
12. [For79] S. Fortune. A note on sparse complete sets. SIAM Journal on Computing, 8:431-433, 1979.
13. [GL89] O. Goldreich, L. Levin. A hard-core predicate for all one-way functions. In Proc. 21st STOC, pages 25-32, 1989.
14. [Har78] J. Hartmanis. On log-tape isomorphisms of complete sets. Theoretical Computer Science, 7(3):273-286, 1978.
15. [HOT94] L. Hemachandra, M. Ogiwara, and S. Toda. Space-efficient recognition of sparse self-reducible languages. Computational Complexity, 4:262-296, 1994.
16. [HOW92] L. Hemachandra, M. Ogiwara, and O. Watanabe. How hard are sparse sets. In Proc. 7th Structures, pages 222-238, 1992.
17. [KV86] M. Karpinski and R. Verbeek. On the Power of Two-Way Random Generators and the Impossibility of Deterministic Poly-Space Simulation. Information and Control, Vol. 71, pages 131-142, 1986.
18. [KL80] R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proc. 12th ACM Symp. on Theory of Computing, pages 302-309, 1980.
19. [Lad75] R. Ladner. The circuit value problem is log space complete for P. SIGACT News, 7(l):18-20, 1975.
20. [LLS75] R. Ladner, N. Lynch, and A. Selman. A comparison of polynomial time reducibilities. Theoretical Computer Science, 1:103-123, 1975.
21. [Mah82] S. Mahaney. Sparse complete sets for NP: solution of a conjecture of Berman and Hartmanis. Journal of Computer and System Sciences, 25:130-143, 1982.
22. [Mul87] K. Mulmuley. A fast parallel algorithm to compute the rank of a matrix over an arbitrary field. Combinatorica, 7(1):101-104, 1987.
23. [NN90] J. Naor and M. Naor. Small-bias probability spaces: efficient constructions and applications. In Proc. 22nd STOC, pages 213-223, 1990.
24. [Ogi95] M. Ogihara. Sparse hard sets for P yield space-efficient algorithms. In Proc. 36th FOCS, pages 354-361, 1995.
25. [OL91] M. Ogiwara and A. Lozano. On one-query self-reducible sets. In Proc. 6th Structures, pages 139-151, 1991.
26. [OW91] M. Ogiwara and O. Watanabe. On polynomial-time bounded truth-table reducibility of NP sets to sparse sets. SIAM Journal on Computing, 20(3):471-483, 1991.
27. [RR92] D. Ranjan and P. Rohatgi. On randomized reductions to sparse sets. In Proc. 7th Structures, pages 239-242, 1992.
28. [VV85] L. Valiant and V. Vazirani. NP is as easy as detecting unique solutions. In Proceedings of 17th ACM Symposium Theory of Computing, pages 458-463, 1985.
29. [vL91] J.H. van Lint. Introduction to Coding Theory. Springer-Verlag, 1991.
30. [vM95] D. van Melkebeek. On Truth-table Hard Sparse sets for P. University of Chicago Technical Report 95-06. 1995.
31. [You92a] P. Young. How reductions to sparse sets collapse the polynomial-time hierarchy: A primer (Part I). SIGACT News, 23(3):107-117, 1992.
32. [You92b] P. Young. How reductions to sparse sets collapse the polynomial-time hierarchy: A primer (Part II). SIGACT News, 23(4):83-94, 1992.