P-selective sets and reducing search to decision vs self-reducibility

Journal of Computer and System Sciences

Volumn 53, Issue 2, 1996, Pages 194-209

  Hemaspaandra, Edith ^a   Naik, Ashish V ^b   Ogihara, Mitsunori ^c   Selman, Alan L ^b  

^a LE MOYNE COLLEGE   (United States)

^b the State University of New York   (United States)

^c University of Rochester   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DECISION THEORY; FORMAL LANGUAGES; POLYNOMIALS; PROBLEM SOLVING; TURING MACHINES;

P SELECTIVE SETS; SEARCH; SELF REDUCIBILITY;

COMPUTATIONAL COMPLEXITY;

EID: 0030263710     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcss.1996.0061     Document Type: Article

References (52)

1. A. Amir, R. Beigel, and W. Gasarch, Cheatable, P-terse, and P-superterse sets, manuscript, Dec. 7, 1989.
2. M. Abadi, J. Feigenbaum, and J. Kilian, On hiding information from an oracle, J. Comput. System Sci. 39 (1989), 21-50.
3. L. Babai, Trading group theory for randomness, in "Proceedings, 17th Annual ACM Symp. on Theory of Computing, 1985," pp. 421-429.
4. J. Balcázar, Self-reducibility structures and solutions of NP problems, Riv. Mat. 4, No. 4 (1990), 431-441.
5. R. Beigel, M. Bellare, J. Feigenbaum, and S. Goldwasser, Languages that are easier than their proofs, in "Proceedings, 32nd IEEE Symp. on Foundations of Computer Science, 1991," pp. 19-28.
6. A. Borodin and A. Demers, "Some Comments on Functional Self-Reducibility and the NP Hierarchy," Technical Report TR76-284, Cornell University, Department of Computer Science, 1976.
7. R. Beigel, "Query-Limited Reducibilities," Ph.D. thesis, Stanford University, 1987.
8. R. Beigel, "NP-Hard Sets are P-Superterse unless R = NP," Technical Report 88-04, Department of Computer Science, Johns Hopkins University, 1988.
9. R. Beigel, Bounded queries to SAT and the Boolean hierarchy, Theor. Comput. Sci. 84, No. 2 (1991), 199-223.
10. P. Berman, Relationships between density and deterministic complexity of NP-complete languages, in "Proceedings, 5th Colloq. on Automata, Languages, and Programming," Lecture Notes in Computer Science, Vol. 62, pp. 63-71, Springer-Verlag, Berlin, 1978.
11. L. Babai, L. Fortnow, and C. Lund, Nondeterministic exponential time has two-prover interactive protocols, Comput. Complexity 1 (1991), 3-40.
12. M. Bellare and S. Goldwasser, The complexity of decision versus search, SIAM J. Comput 23, No. 1 (1994), 97-119.
13. M. Blum and S. Kannan, Designing programs that check their work, J. Assoc. Comput. Mach. 42, No. 1 (1995), 269-291.
14. R. Book, T. Long, and A. Selman, Quantitative relativizations of complexity classes, SIAM J. Comput. 13, No. 3 (1984), 461-487.
15. M. Ben-Or, S. Goldwasser, J. Kilian, and A. Wigderson, Multi-prover interactive proofs: How to remove intractability assumptions, in "Proceedings, 20th Annual ACM Symp. Theory of Computing, 1988," pp. 113-131.
16. R. Book, Tally languages and complexity classes, Inform. and Control 26 (1974), 186-193.
17. H. Buhrman and T. Thierauf, The complexity of generating and checking proofs of membership, in "Proceedings 13th Symp. on Theoretical Aspects of Computer Science," Lecture Notes in Computer Science, Vol. 1046, pp. 75-86, Springer-Verlag, Berlin, 1996.
18. H. Buhrman, P. van Helden, and L. Torenvliet, P-selective self-reducible sets: A new characterization of P, in Proceedings, 8th Annual Conference on Structure in Complexity Theory, 1993," pp. 44-51.
19. J. Cai, A. Condon, and R. Lipton, PSPACE is provable by two provers in one round, J. Comput. System Sci. 48 (1994), 183-193.
20. J Feigenbaum and L. Fortnow, On the random-self-reducibility of complete sets, SIAM J. Comput. 22 (1993), 994-1005.
21. J. Feigenbaum, L. Fortnow, C. Lund, and D. Spielman, The power of adaptiveness and additional queries in random-self-reductions, Comp. Complexity 4 (1994), 158-174.
22. S. Fenner, S. Homer, M. Ogiwara, and A Selman, On using oracles that compute values, in "Proceedings, 10th Annual Symp. on Theoret. Aspects of Computer Science," Lecture Notes in Computer Science, Vol. 665, pp. 398-407, Springer-Verlag, New York/Berlin, 1993.
23. U. Feige and L. Lovász, Two-prover one-round proof systems: Their power and their problems, in "Proceedings, 25th Annual Symposium on Theory of Computing, 1992," pp. 733-744.
24. S. Fortune, A note on sparse complete sets, SIAM J. Comput. 8 (1979), 431-433.
25. L. Fortnow, J. Rompel, and M. Sipser, On the power of multi-prover interactive protocols, in "Proceedings, 3rd Annual Conference on Structure in Complexity Theory," pp. 156-161, IEEE Comput. Soc., Los Alamitos, CA, 1988.
26. S. Goldwasser, S. Micali, and C. Rackoff, The knowledge complexity of interactive proof systems, SIAM J. Comput. 18, No. 1 (1989), 186-208.
27. J. Grollmann and A. Selman, Complexity measures for public-key cryptosystems, SIAM J. Comput. 17, No. 2 (1988), 309-355.
28. L. Hemachandra, A. Hoesne, M. Ogiwara, A. Selman, T. Thierauf, and J. Wang, Selectivity, in "Proceedings, 5th International Conference on Computing and Information," pp. 55-59, IEEE Comput. Soc., Los Alamitos, CA, 1993.
29. R. Impagliazzo and G. Tardos, Search versus decision in super-polynomial time, in "Proceedings, IEEE Foundations of Computer Science, 1991," pp. 222-227.
30. C. Jockusch, Jr., Semirecursive sets and positive reducibility, Trans. Am. Math. Soc. 131, No. 2 (1968), 420-436.
31. D. Joseph and P. Young, Self-reducibility: The effects of internal structure on computational complexity, in "Complexity Theory Retrospective" (A. Selman, Ed.), pp. 82-107, Springer-Verlag, New York, 1990.
32. K. Ko, On self-reducibility and weak P-selectivity, J. Comput. System Sci. 26 (1983), 209-211.
33. K. Ko, On helping by robust oracle machines, Theor. Comput. Sci. 52 (1987), 15-36.
34. M. Krentel, The complexity of optimization problems, J. Comput. System Sci. 36 (1988), 490-509.
35. C. Lund, L. Fortnow, H. Karloff, and N. Nisan, Algebraic methods for interactive proof systems, J. Assoc. Comput. Mach. 39, No. 4 (1992), 859-868.
36. R. Ladner, N. Lynch, and A. Selman, A comparison of polynomial time reducibilities, Theor. Comput. Sec. 1 (1975), 103-123.
37. S. Mahaney, Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis, J. Comput. System Sci. 25 (1982), 130-142.
38. G. Miller, Reimann's hypothesis and tests for primality, J. Comput. System Sci. 13 (1976), 300-317.
39. A. Meyer and M. Paterson, "With What Frequency are Apparently Intractable Problems Ddifficult?" Technical Report MIT/LCS/TM-126, MIT, 1979.
40. A. Naik, M. Ogiwara, and A. Selman, P-selective sets, and reducing search to decision vs self-reducibility, in "Proceedings, 8th Annual Conference on Structure in Complexity Theory," pp. 52-64, IEEE Comput. Soc., Los Alamitos, CA, 1993.
41. U. Schöning, Robust algorithms: A different approach to Oracles, Theor. Comput Sci. 40 (1985), 57-66.
42. A. Selman, P-selective sets, tally languages, and the behavior of polynomial time reducibilities on NP, Math. Systems Theory 13 (1979), 55-65.
43. A. Selman, Analogues of semirecursive sets and effective reducibilities to the study of NP complexity, Inform. and Control 52, No. 1 (1982), 36-51.
44. A. Selman, Reductions on NP and P-selective sets, Theor. Comput. Sci. 19 (1982), 287-304.
45. A. Selman, Natural self-reducible sets, SIAM J. Comput. 17 (1988), 989-996.
46. A. Selman, A taxonomy of complexity classes of functions, J. Comput. System Sci. 48, No. 2 (1994), 357-381.
47. A. Shamir, IP = PSPACE, J. Assoc. Comput. Mach. 39, No. 4 (1992), 869-877.
48. T. Thierauf, personal communication, 1992.
49. S. Toda, On polynomial-time truth-table reducibilities of intractable sets to P-selective sets, Math. Systems Theory 24 (1991), 69-82.
50. B. Trahtenbrot, On autoreducibility, Dokl. Akad. Nauk SSSR 192 (1970); translation in Soviet Math. Dokl. 11 (1970), 814-817.
51. B. Trahtenbrot, On autoreducibility, Dokl. Akad. Nauk SSSR 192 (1970); translation in Soviet Math. Dokl. 11 (1970), 814-817.
52. O. Watanabe and S. Toda, Structural analysis of the complexity of inverse functions, Math. Systems Theory 26 (1993), 203-214.