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P-Immune Sets with Holes Lack Self-Reducibility Properties

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Combinatorics, Computability and Logic

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

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Abstract

No P-immune set having exponential gaps is positive-Turing self-reducible.

Supported in part by grants NSF-INT-9815095/DAAD-315-PPP-gü-ab and NSFCCR-9322513.

Supported in part by grant NSF-INT-9815095/DAAD-315-PPP-gü-ab. Work done while visiting the University of Rochester.

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References

  1. K. Ambos-Spies and J. Kämper. On disjunctive self-reducibility. In Proceedings of the 2nd Workshop on Computer Science Logic, pages 1–13. Springer-Verlag Lecture Notes in Computer Science #385, October 1988.

    Google Scholar 

  2. J. Balcazar. Self-reducibility. Journal of Computer and System Sciences, 41 (3): 367–388, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Balcazar, J. Díaz, and J. Gabarró. Structural Complexity I. EATCS Texts in Theoretical Computer Science. Springer-Verlag, 2nd edition, 1995.

    Google Scholar 

  4. L. Berman. On the structure of complete sets. In Proceedings of the 17th IEEE Symposium on Foundations of Computer Science, pages 76–80, 1976.

    Google Scholar 

  5. C. Bennett and J. Gill. Relative to a random oracle A, PA ≠ NPA ≠ coNPA with probability 1. SIAM Journal on Computing, 10: 96–113, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  6. J. Goldsmith, L. Hemachandra, D. Joseph, and P. Young. Near-testable sets. SIAM Journal on Computing, 20 (3): 506–523, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  7. L. Hemachandra and S. Jain. On the limitations of locally robust positive reductions. International Journal of Foundations of Computer Science, 2 (3): 237–255, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Hartmanis and Y. Yesha. Computation times of NP sets of different densities. Theoretical Computer Science, 34: 17–32, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Hemaspaandra and M. Zimand. Strong self-reducibility precludes strong immunity. Mathematical Systems Theory, 29 (5): 535–548, 1996.

    MathSciNet  MATH  Google Scholar 

  10. D. Joseph and P. Young. Self-reducibility: Effects of internal structure on computational complexity. In A. Selman, editor, Complexity Theory Retrospective, pages 82–107. Springer-Verlag, 1990.

    Google Scholar 

  11. J. Kämper. A result relating disjunctive self-reducibility to P-immunity. Information Processing Letters, 33 (5): 239–242, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. Karp and R. Lipton. Some connections between nonuniform and uniform complexity classes. In Proceedings of the 12th ACM Symposium on Theory of Computing, pages 302–309. ACM Press, April 1980. An extended version has also appeared as: Turing machines that take advice, L’Enseignement Mathématique, 2nd series, 28, 1982, pages 191–209.

    Google Scholar 

  13. K. Ko and D. Moore. Completeness, approximation, and density. SIAM Journal on Computing, 10 (4): 787–796, 1981.

    Article  MathSciNet  MATH  Google Scholar 

  14. R. Ladner, N. Lynch, and A. Selman. A comparison of polynomial time reducibilities. Theoretical Computer Science, 1 (2): 103–124, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  15. A. Meyer and M. Paterson. With what frequency are apparently intractable problems difficult? Technical Report MIT/LCS/TM-126, Laboratory for Computer Science, MIT, Cambridge, MA, 1979.

    Google Scholar 

  16. C. Papadimitriou. Computational Complexity. Addison-Wesley, 1994.

    Google Scholar 

  17. H. Rogers, Jr. The Theory of Recursive Functions and Effective Computability. McGraw-Hill, 1967.

    Google Scholar 

  18. C. Schnorr. Optimal algorithms for self-reducible problems. In Proceedings of the 3rd International Colloquium on Automata, Languages, and Programming, pages 322–337, July 1976.

    Google Scholar 

  19. A. Selman. Reductions on NP and P-selective sets. Theoretical Computer Science, 19 (3): 287–304, 1982.

    Article  MathSciNet  MATH  Google Scholar 

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© 2001 Springer-Verlag London Limited

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Hemaspaandra, L.A., Hempel, H. (2001). P-Immune Sets with Holes Lack Self-Reducibility Properties. In: Calude, C.S., Dinneen, M.J., Sburlan, S. (eds) Combinatorics, Computability and Logic. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0717-0_10

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  • DOI: https://doi.org/10.1007/978-1-4471-0717-0_10

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-526-7

  • Online ISBN: 978-1-4471-0717-0

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