Cook versus Karp-Levin: Separating completeness notions if NP is not small

Theoretical Computer Science

Volumn 164, Issue 1-2, 1996, Pages 141-163

  Lutz, Jack H ^a   Mayordomo, Elvira ^b  

^a Iowa State University   (United States)

^b UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; COMPUTER PROGRAMMING LANGUAGES; POLYNOMIALS; PROBLEM SOLVING; THEOREM PROVING;

CLASS SEPARATION; COOK COMPLETE; KARP-LEVIN COMPLETENESS; TRUTH TABLE REDUCIBILITIES;

COMPUTATIONAL COMPLEXITY;

EID: 0030246728     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/0304-3975(95)00189-1     Document Type: Article

References (29)

1. M. Bellare and S. Goldwasser, The complexity of decision versus search, SIAM J. Comput. 23 (1994) 97-119.
2. L. Berman and J. Hartmanis, On isomorphism and density of NP and other complete sets, SIAM J. Comput. 6 (1977) 305-322.
3. R.V. Book, Tally languages and complexity classes, Inform. and Control 26 (1974) 186-193.
4. H. Buhrman, S. Homer and L. Torenvliet, Completeness for nondeterministic complexity classes, Math. Systems Theory 24 (1991) 179-200.
5. S.A. Cook, The complexity of theorem proving procedures, Proc. Third ACM Symp on the Theory of Computing (1971) 151-158.
6. S. Homer, Structural properties of nondeterministic complete sets, Proc. Fifth Annual Structure in Complexity Theory Conf. (1990) 3-10.
7. D.W. Juedes and J.H. Lutz, The complexity and distribution of hard problems, SIAM J. Comput. 24 (1995) 279-295.
8. R.M. Karp, Reducibility among combinatorial problems, in: R.E. Miller and J.W. Thatcher, eds., Complexity of Computer Computations (Plenum, New York, 1972) 85-104.
9. K. Ko and D. Moore, Completeness, approximation and density, SIAM J. Comput. 10 (1981) 787-796.
10. R. Ladner, N. Lynch and A. Selman, A comparison of polynomial-time reducibilities, Theoret Comput Sci 1 (1975) 103-123.
11. L.A. Levin, Universal sequential search problems, Problems of Information Transmission 9 (1973) 265-266.
12. L. Longpré and P. Young, Cook reducibility is faster than Karp reducibility in NP, J. Comput. System Sci. 41 (1990) 389-401.
13. J.H. Lutz, Almost everywhere high nonuniform complexity, J. Comput. System Sci. 44 (1992) 220-258.
14. J.H. Lutz, Resource-bounded measure, in preparation.
15. J.H. Lutz and E. Mayordomo, Measure, stochasticity, and the density of hard languages, SIAM J. Comput. 23 (1994) 762-779.
16. E. Mayordomo, Almost every set in exponential time is P-bi-immune, Theoret. Comput. Sci. 136 (1994) 487-506.
17. A.R. Meyer (1977) reported in [2].
18. M. Ogiwara and O. Watanabe, On polynomial bounded truth-table reducibility of NP sets to sparse sets, SIAM J. Comput. 20 (1991) 471-483.
19. P. Orponen and U. Schöning, The density and complexity of polynomial cores for intractable sets, Inform. and Control 70 (1986) 54-68.
20. C.P. Schnorr, Klassifikation der Zufallsgesetze nach Komplexität und Ordnung, Z. Wahrscheinlichkeitstheorie verw. Geb. 16 (1970) 1-21.
21. C.P. Schnorr, A unified approach to the definition of random sequences, Math. Systems Theory 5 (1971) 246-258.
22. C.P. Schnorr, Zufälligkeit und Wahrscheinlichkeit, Lecture Notes in Mathematics, Vol. 218 (Springer, Berlin, 1971).
23. C.P. Schnorr, Process complexity and effective random tests, J. Comput. System Sci. 7 (1973) 376-388.
24. A.L. Selman, P-selective sets, tally languages, and the behavior of polynomial time reducibilities on NP, Math. Systems Theory 13 (1979) 55-65.
25. A.L. Selman, Reductions on NP and P-selective sets, Theoret. Comput. Sci. 19 (1982) 287-304.
26. O. Watanabe, A comparison of polynomial time completeness notions, Theoret. Comput. Sci. 54 (1987) 249-265.
27. O. Watanabe, On the Structure of Intractable Complexity Classes, PhD thesis, Tokyo Institute of Technology, 1987.
28. O. Watanabe and S. Tang, On polynomial time Turing and many-one completeness in PSPACE, Theoret. Comput. Sci. 97 (1992) 199-215.
29. P. Young, Some structural properties of polynomial reducibilities and sets in NP, Proc. Fifteenth ACM Symp. on Theory of Computing (1983) 392-401.