Skip to main content

Probabilistic machines, oracles, and quantifiers

  • Conference paper
  • First Online:
Recursion Theory Week

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1141))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Angluin, D., On counting problems and the polynomialtime hierarchy, Theor. Computer Science 12 (1980) 161–173.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bach, E., Miller, G., and Shallit, J., Sums of divisors, perfect numbers, and factoring, Proceedings of the 16th annual ACM Symposium on the Theory of Computing (1984) 183–190.

    Google Scholar 

  3. Baker, T., Gill, J., and Solovay, R., Relativization of the P=? NP question, SIAM J. of Computing 4 (1975) 431–442.

    Article  MathSciNet  MATH  Google Scholar 

  4. Baker, T. and Selman, A., A second step toward the polynomial hierarchy, Theoretical Computer Science 8 (1979) 177–187.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bennett, C.H. and Gill, J., Relative to a random oracle A, with probability 1, SIAM J. Computing 10 (1981) 96–113.

    Article  MathSciNet  MATH  Google Scholar 

  6. Cook, S.A., The complexity of theorem-proving procedures. Proc. 3rd annual ACM Symp. on Theory of Computing, Association for Computing Machinery, New York, NY, 151–158.

    Google Scholar 

  7. Gill, J., Computational complexity of probabilistic Turing machines, SIAM J. of Computing 6 (1977) 675–695.

    Article  MathSciNet  MATH  Google Scholar 

  8. Heller, H., On relativized exponential and probabilistic complexity classes, submitted to Information and Control.

    Google Scholar 

  9. Hopcroft, J. and Ullman, J., Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, MA, 1979, x+418 pp.

    MATH  Google Scholar 

  10. Hunt, J.W., Topics in Probabilistic Complexity, Ph.D. Dissertation, Department of Electrical Engineering, Stanford University, Stanford, CA, 1978.

    Google Scholar 

  11. Rabin, M., Probabilistic algorithm for testing primality, J. of Number Theory 12 (1980) 128–138.

    Article  MathSciNet  MATH  Google Scholar 

  12. Rackoff, C., Relativized questions involving probabilistic algorithms, JACM 29 (1982) 261–268.

    Article  MathSciNet  MATH  Google Scholar 

  13. Simon, J., On some central problems in computational complexity, Ph.D. Dissertation, Department of Computer Science, Cornell University, Ithaca, NY, 1975.

    Google Scholar 

  14. Solovay, R., and Strassen, V., A fast Monte-Carlo test for primality, SIAM J. of Computing 6 (1977) 84–85.

    Article  MathSciNet  MATH  Google Scholar 

  15. Stockmeyer, L.J., The polynomial-time hierarchy, Theor. Computer Science 3 (1976) 1–22.

    Article  MathSciNet  MATH  Google Scholar 

  16. Wrathall, C., Complete sets and the polynomial-time hierarchy, Theor. Computer Science 3 (1976) 23–33.

    Article  MathSciNet  MATH  Google Scholar 

  17. Zachos, S., Robustness of probabilistic computational complexity classes under definitional perturbations, Information and Control 54 (1982) 143–154.

    Article  MathSciNet  MATH  Google Scholar 

  18. Zachos, S. and Heller, H., A decisive characterization of BPP, submitted to Information and Control.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Heinz-Dieter Ebbinghaus Gert H. Müller Gerald E. Sacks

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Hinman, P.G., Zachos, S. (1985). Probabilistic machines, oracles, and quantifiers. In: Ebbinghaus, HD., Müller, G.H., Sacks, G.E. (eds) Recursion Theory Week. Lecture Notes in Mathematics, vol 1141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076220

Download citation

  • DOI: https://doi.org/10.1007/BFb0076220

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15673-4

  • Online ISBN: 978-3-540-39596-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics