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Some remarks on polynomial time isomorphisms

  • Jie Wang
Theory Of Computing, Algorithms And Programming
Part of the Lecture Notes in Computer Science book series (LNCS, volume 468)

Abstract

Joseph and Young [JY-85] hypothesized that the Berman-Hartmanis isomorphism conjecture fails if there exists a k-completely creative set in NP with no p-invertible p-completely productive functions. We verify this hypothesis for DEXT based on new results of p-creative sets in [Wan-89]. In particular, we prove that the isomorphism conjecture for DEXT fails iff there is a p-creative set for P in DEXT with no p-invertible p-productive functions.

Keywords

Polynomial Time Turing Machine Deterministic Turing Machine Nondeterministic Turing Machine Polynomial Time Computable Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [Ber-77]
    L. Berman, Polynomial reducibilities and complete sets, Ph.D. thesis, Cornell University, 1977.Google Scholar
  2. [Ga-89]
    K. Ganesan, Complete problems, creative sets and isomorphism conjectures, Ph.D. thesis, Boston University, 1989.Google Scholar
  3. [GS-88]
    J. Grollmann and A. Selman, Complexity measures for public-key cryptosystems, SIAM J. Comput., 17(1988) 309–335.Google Scholar
  4. [JY-85]
    D. Joseph and P. Young, Some remarks on witness functions for nonpolynomial and noncomplete sets in NP, Theoret. Comput. Sci., 39(1985) 225–237.Google Scholar
  5. [KLD-86]
    K. Ko, T. Long, and D. Du, A note on one-way functions and polynomial-time isomorphisms, Theoretical Computer Science, 47(1986) 263–276.Google Scholar
  6. [KMR-86]
    S. Kurtz, S. Mahaney, and J. Royer, Collapsing Degrees, University of Chicago, TR-86-006, 1986.Google Scholar
  7. [MY-85]
    S. Mahaney and P. Young, Reductions among polynomial isomorphism types, Theoretical Computer Science, 39(1985) 207–224.Google Scholar
  8. [My-55]
    J. Myhill, Creative Sets, ZML 1(1955) 97–103.Google Scholar
  9. [Ro-67]
    H. Rogers, Theory of Recursive Functions and Effective Computability, McGraw-Hill Book, 1967.Google Scholar
  10. [Wan-89]
    J. Wang, On p-creative sets and p-completely creative sets, to appear in Theoretical Computer Science. The earlier version of this paper appeared in IEEE Proceedings of the 4th Annual Conference on Structure in Complexity Theory, June 1989, 24–33.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Jie Wang
    • 1
  1. 1.Computer Science Department, CLABoston UniversityBoston

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