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A uniform reduction theorem extending a result of J. Grollmann and A. Selman

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Automata, Languages and Programming (ICALP 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 226))

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Abstract

We derive a recursion-theoretic result telling when a family of reductions to a class

can be replaced by a single oracle Turing machine. The theorem is a close analogue of the Uniform Boundedness Theorem of functional analysis, specializing it to the Cantor-set topology on ℙ(Σ*). This generalizes one of the main theorems of J. Grollmann and A. Selman [FOCS '84], namely that NP-hardness implies uniform NP-hardness for ‘promise problems’. We investigate other consequences and problems arising from the theorem.

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References

  1. K. Ambos-Spies. Sublattices of the polynomial-time degrees. Information and Control 65, No. 1, April 1985, pp 63–84.

    Google Scholar 

  2. D. Angluin. Counting problems and the polynomial-time hierarchy. Theoretical Computer Science 12, No. 2, October 1980.

    Google Scholar 

  3. N. Cutland. Computability. (Cambridge: Camb. University Press, 1980.)

    Google Scholar 

  4. M. Dowd. Forcing and the P hierarchy. Preprint, Rutgers Univ., 1982.

    Google Scholar 

  5. M. Dummett. Elements of Intuitionism. (Oxford: Clarendon Press, 1977.)

    Google Scholar 

  6. S. Even and Y. Yacobi. Cryptography and NP-completeness. Proc. ICALP '80, Springer LNCS 80, pp. 195–207.

    Google Scholar 

  7. J. Grollmann. Ph.D dissertation, Univ. of Dortmund, W. Germany, 1984.

    Google Scholar 

  8. J. Grollmann and A. Selman. Complexity measures for public-key cryptosystems. Proc. 25th FOCS, Oct. 1984.

    Google Scholar 

  9. Ibid. Iowa State Univ. Technical Report TR 85-31, November 1985.

    Google Scholar 

  10. S. Homer. Minimal degrees for polynomial reducibilities. Draft, Boston University, 1982.

    Google Scholar 

  11. D. Kozen and M. Machtey. On relative diagonals. TR RC 8184 (#35583), IBM Thomas J. Watson Research Center, Yorktown Hts., NY 10598 USA, 1980.

    Google Scholar 

  12. R. Ladner. On the structure of polynomial-time reducibility. J. ACM 22, 1975, pp. 155–171.

    Google Scholar 

  13. K. Melhorn. On the size of sets of computable functions. Proc. 14th Symposium on Switching and Automata Theory (now STOC), 1973, pp 190–196.

    Google Scholar 

  14. H. Rogers. Theory of Recursive Functions and Effective Computability. (New York: McGraw-Hill, 1967).

    Google Scholar 

  15. H. Royden. Real Analysis. (New York: The MacMillan Company, 1963).

    Google Scholar 

  16. W. Rudin. Real and Complex Analysis (2nd. edition). (New York: McGraw-Hill, 1974.)

    Google Scholar 

  17. A. Selman. Reductions on NP and P-selective sets. Theoretical Computer Science 19, 1982, pp 287–304.

    Google Scholar 

  18. A. Selman and Y. Yacobi. The complexity of promise problems. Proc. ICALP '82, Springer LNCS 140, 1982, pp. 502–509.

    Google Scholar 

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Authors and Affiliations

  1. Merton College, OX1 4JD, Oxford, England

    Kenneth W. Regan

Authors
  1. Kenneth W. Regan
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Editor information

Laurent Kott

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© 1986 Springer-Verlag Berlin Heidelberg

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Regan, K.W. (1986). A uniform reduction theorem extending a result of J. Grollmann and A. Selman. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_82

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  • DOI: https://doi.org/10.1007/3-540-16761-7_82

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16761-7

  • Online ISBN: 978-3-540-39859-2

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