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On random hard sets for NP

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Algorithms and Computation (ISAAC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 834))

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Abstract

The problem of whether NP has a random hard set (i.e., a set in RAND) is investigated. We show that for all recursive oracle A such that PA ≠ NPA, NPA has no hard set in RAND. On the other hand, we also show that for almost all oracle A, PA ≠ NPA and NPA has a hard set in RAND.

Part of this research was done while the second author was visiting Department of Mathematics, University of California at Santa Barbara. This research is supported in part by NSF grant CCR-9302057.

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References

  1. J. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity I, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, 1988.

    Google Scholar 

  2. J. Balcázar, J. Díaz, and J. Gabarró. Structural Complexity II, EATCS Monographs on Theoretical Computer Science, Springer-Verlag, 1991.

    Google Scholar 

  3. C. Bennett and J. Gill, Relative to a random oracle A, PA ≠ NPA ≠ co-NPA with probability 1, SIAM J. Comput. 10 (1981), 96–113.

    Article  Google Scholar 

  4. R. Book, J. Lutz, and K. Wagner, An observation on probability versus randomness with applications to complexity classes, Math. Systems Theory 26 (1994), 201–209.

    Google Scholar 

  5. G. Chaitin, A theory of program size formally identical to information theory, J. Assoc. Comput. Mach. 22 (1975), 329–340.

    Google Scholar 

  6. D. Juedes, J. Lathrop, and J. Lutz, Computational depth and reducibility, Theoret. Comput. Sci. (1995), to appear.

    Google Scholar 

  7. L. Levin, Laws of information conservation (nongrowth) and aspects of the foundations of probability theory, Problems of Information Transmission 10 (1974), 206–210.

    Google Scholar 

  8. M. Li and P. Vitányi, An Introduction to Kolmogorov Complexity and Its Applications, Springer-Verlag, 1993.

    Google Scholar 

  9. P. Martin-Löf, On the definition of random sequences, Info. Control 9 (1966), 602–619.

    Google Scholar 

  10. C. Schnorr, Process complexity and effective random tests, J. Computer System Sci. 7 (1973), 376–388.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Mathematics, University of California, 93106, Santa Barbara, CA, USA

    Ronald V. Book

  2. Dept. of Computer Science, Tokyo Institute of Technology, Meguro-ku Ookayama, 152, Tokyo, Japan

    Osamu Watanabe

Authors
  1. Ronald V. Book
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  2. Osamu Watanabe
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Editor information

Ding-Zhu Du Xiang-Sun Zhang

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© 1994 Springer-Verlag Berlin Heidelberg

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Book, R.V., Watanabe, O. (1994). On random hard sets for NP. In: Du, DZ., Zhang, XS. (eds) Algorithms and Computation. ISAAC 1994. Lecture Notes in Computer Science, vol 834. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58325-4_165

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  • DOI: https://doi.org/10.1007/3-540-58325-4_165

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58325-7

  • Online ISBN: 978-3-540-48653-4

  • eBook Packages: Springer Book Archive

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