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One-Sided Versus Two-Sided Error in Probabilistic Computation

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STACS 99 (STACS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1563))

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Abstract

We demonstrate how to use Lautemann’s proof that BPP is in Σ2 p to exhibit that BPP is in RP PromiseRP. Immediate consequences show that if PromiseRP is easy or if there exist quick hitting set generators then P = BPP. Our proof vastly simplifies the proofs of the later result due to Andreev, Clementi and Rolim and Andreev,

Clementi, Rolim and Trevisan.

Clementi, Rolim and Trevisan question whether the promise is necessary for the above results, i.e., whether BPP ⊂-RP RP for instance. We give a relativized world where P = RP ≠ BPP and thus the promise is indeed needed.

Partially supported by the European Union through NeuroCOLT ESPRIT Working Group Nr. 8556, and HC&M grant nr. ERB4050PL93-0516.

Supported in part by NSF grant CCR 92-53582.

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References

  1. A. Andreev, A. Clement, and J. Rolim. A new derandomization method. Journal of the ACM, 45(1):179–213, Januari 1998.

    Google Scholar 

  2. A. Andreev, A. Clement, J. Rolim, and L. Trevisan. Weak random sources, hittings sets, and BPP simulations. In Proceedings of the 38th IEEE Symposium on Foundations of Computer Science, pages 264–272. IEEE, New York, 1997.

    Chapter  Google Scholar 

  3. M. Blum and R. Impagliazzo. Generic oracles and oracle classes. In Proceedings of the 28th IEEE Symposium on Foundations of Computer Science, pages 118–126. IEEE, New York, 1987.

    Google Scholar 

  4. A. Clementi, J. Rolim, and L. Trevisan. Recent advances towards proving BPP = P. Bulletin of the European Association for Theoretical Computer Science, 64:96–103, February 1998.

    Google Scholar 

  5. S. Fenner, L. Fortnow, S. Kurtz, and L. Li. An oracle builder’s toolkit. In Proceedings of the 8th IEEE Structure in Complexity Theory Conference, pages 120–131. IEEE, New York, 1993.

    Google Scholar 

  6. J. Grollmann and A Selman. Complexity measures for public-key cryptosystems. SIAM Journal on Computing, 17:309–355, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. Heller. On relativized exponential and probabilistic complexity classes. Information and Computation, 71:231–243, 1986.

    MATH  MathSciNet  Google Scholar 

  8. R. Impagliazzo and M. Naor. Decision trees and downward closures. In Proceedings of the 3rd IEEE Structure in Complexity Theory Conference, pages 29–38. IEEE, New York, 1988.

    Chapter  Google Scholar 

  9. C. Lautemann. BPP and the polynomial hierarchy. Information Processing Letters, 17(4):215–217, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  10. N. Nisan. CREW PRAMSs and decision trees. SIAM Journal on Computing, 20(6):999–1007, December 1991.

    Google Scholar 

  11. M. Sipser. A complexity theoretic approach to randomness. In Proceedings of the 15th ACM Symposium on the Theory of Computing, pages 330–335. ACM, New York, 1983.

    Google Scholar 

  12. S. Zachos. Probabilistic quantifiers and games. Journal of Computer and System Sciences, 36:433–451, 1988.

    Article  MATH  MathSciNet  Google Scholar 

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Buhrman, H., Fortnow, L. (1999). One-Sided Versus Two-Sided Error in Probabilistic Computation. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_9

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  • DOI: https://doi.org/10.1007/3-540-49116-3_9

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  • Print ISBN: 978-3-540-65691-3

  • Online ISBN: 978-3-540-49116-3

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