One-Sided Versus Two-Sided Error in Probabilistic Computation
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.
Unable to display preview. Download preview PDF.
- [ACR98]A. Andreev, A. Clement, and J. Rolim. A new derandomization method. Journal of the ACM, 45(1):179–213, Januari 1998.Google Scholar
- [BI87]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
- [CRT98]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
- [FFKL93]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
- [Nis91]N. Nisan. CREW PRAMSs and decision trees. SIAM Journal on Computing, 20(6):999–1007, December 1991.Google Scholar
- [Sip83]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