Honest iteration schemes of randomizing algorithms
This paper further studies Blass and Gurevich's iteration schemes of randomizing algorithms for randomized reductions [BG91]. An iteration scheme of a randomizing algorithm is honest if it passes a bit to a process independently of its value. We show that if a fair iteration scheme is honest, then it is independent. This implies the previous known sufficient condition for independence in [BG91]. On the other hand, we show that for independence, honesty is not necessary.
KeywordsTuring Machine Initial Segment Search Problem Iteration Scheme Fair Coin
Unable to display preview. Download preview PDF.
- [BCGL89]S. Ben-David, B. Chor, O. Goldreich, and M. Luby, On the theory of average case complexity, Proc. 21st Annual ACM Symposium on Theory of Computing, 1989, pp.204–216.Google Scholar
- [BG91]A. Blass and Y. Gurevich, Randomizing reductions of search problems, Proceedings of Foundations of Software Technology and Theoretical Computer Science (Invited Talk), New Delhi, India, 1991, pp. 10–24.Google Scholar
- [IL90]R. Impagliazzo and L. Levin, No better ways to generate hard NP instances than picking uniformly at random, Proc. 31th IEEE Symposium on Foundations of Computer Science, 1990, pp. 812–821.Google Scholar
- [VL88]R. Venkatesan and L. Levin, Random instances of a graph coloring problem are hard, Proc. 20th ACM Symposium on Theory of Computing, 1988, pp. 217–222.Google Scholar
- [Ven91]R. Venkatesan, Average Case Intractability, Ph.D. thesis, Computer Science Department, Boston University, 1991.Google Scholar
- [VR92]R. Venkatesan and S. Rajagopalan, Average case intractability of Diophantine and matrix problems, Proc. of 24th ACM Symposium of Theory of Computing, May 1992, pp. 632–642.Google Scholar
- [WB92]J. Wang and J. Belanger, On average P vs. average NP, Proc. of the 7th IEEE Conference on Structure in Complexity Theory, June 1992, pp. 318–326.Google Scholar