The isomorphism conjecture holds relative to an oracle

SIAM Journal on Computing

Volumn 25, Issue 1, 1996, Pages 193-206

  Fenner, Stephen ^a   Fortnow, Lance ^b   Kurtz, Stuart A ^b  

^a UNIVERSITY OF SOUTHERN MAINE   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Computational complexity; Isomorphism conjecture; Relativization

Indexed keywords

COMPLEXITY CLASS; GENERIC SET; ISOMORPHISM; ORACLE;

COMPUTATIONAL COMPLEXITY;

EID: 0029746517     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539793248305     Document Type: Article

References (21)

1. L. BERMAN AND J. HARTMANIS, On isomorphism and density of NP and other complete sets, in Proc. 8th ACM Symposium on the Theory of Computing, ACM, New York, 1976, pp. 30-40.
2. _, On isomorphism and density of NP and other complete sets, SIAM J. Comput., 1 (1977), pp. 305-322.
3. M. BLUM AND R. IMPAGLIAZZO, Generic oracles and oracle classes, in Proc. 28th IEEE Symposium on Foundations of Computer Science, IEEE, New York, 1987, pp. 118-126.
4. S. COOK, The complexity of theorem-proving procedures, in Proc. 3rd ACM Symposium on the Theory of Computing, ACM, New York, 1971, pp. 151-158.
5. S. FENNER, L. FORTNOW, S. KURTZ, AND L. LI, An oracle builder's toolkit, in Proc. 8th IEEE Structure in Complexity Theory Conference, IEEE, New York, 1993, pp. 120-131.
6. J. GOLDSMITH AND D. JOSEPH, Three results on the polynomial isomorphism of complete sets, in Proc. 27th IEEE Symposium on Foundations of Computer Science, IEEE, New York, 1986, pp. 390-397.
7. J. GROLLMANN AND A. SELMAN, Complexity measures for public-key cryptosystems, SIAM J. Comput., 17 (1988), pp. 309-355.
8. J. HARTMANIS AND L. HEMACHANDRA, One-way functions and the nonisomorphism of NP-complete sets, Theoret. Comput. Sci., 81 (1991), pp. 155-163.
9. S. HOMER AND A. SELMAN, Oracles for Strutural properties: The isomorphism problem and public-key cryptography, in Proc. 4th IEEE Structure in Complexity Theory Conference, IEEE, New York, 1989, pp. 3-14.
10. _, Oracles for structural properties: The isomorphism problem and public-key cryptography, J. Comput. System Sci., 44 (1992), pp. 287-301.
11. D. JOSEPH AND P. YOUNG, Self-reducibility: Effects of internal structure on computational complexity, in Complexity Theory Retrospective, A. Selman, ed., Springer-Verlag, Berlin, New York, 1990, pp. 82-107.
12. S. KURTZ, The isomorphism conjecture fails relative to a generic oracle, Tech. report 88-018, Department of Computer Science, University of Chicago, 1988.
13. S. KURTZ, S. MAHANEY, AND J. ROYER, Progress on collapsing degrees, in Proc. 2nd IEEE Structure in Complexity Theory Conference, IEEE, New York, 1987, pp. 126-131.
14. _, Collapsing degrees, J. Comput. System Sci., 37 (1988), pp. 247-268.
15. _, The structure of complete degrees, in Complexity Theory Retrospective, A. Selman, ed., Springer-Verlag, Berlin, New York, 1990, pp. 82-107.
16. _, The isomorphism conjecture fails relative to a random oracle, J. Assoc. Comput. Mach., (1995), to appear.
17. M. Li AND P. VITÁNYI, An Introduction to Kolmogorov Complexity and Its Applications, Texts and Monographs in Computer Science, Springer, New York, 1993.
18. C. RACKOFF, Relativized questions involving probablistic algorithms, J. Assoc. Comput. Mach., 29 (1982), pp. 261-268.
19. H. ROGERS, Theory of Recursive Functions and Effective Computability, MIT Press, Cambridge, MA, 1987.
20. G. SACKS, Forcing with perfect closed sets, Proc. Sympos. Pure Math., 13 (1971), pp. 331-356.
21. J. ROGERS, The isomorphism conjecture holds and one-way functions exist relative to an oracle, in Proc. 10th IEEE Structure in Complexity Theory Conference, IEEE, New York, 1995, pp. 90-101.