On the improbability of reaching Byzantine agreements

  • Authors:

  • R. L. Graham;A. C. Yao

  • Affiliations:

  • AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, New Jersey;Department of Computer Science,Princeton University, Princeton, New Jersey

  • Venue:
  • STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
  • Year:
  • 1989

Quantified Score

Hi-index 0.00

Visualization

Abstract

It is well known that for the Byzantine Generals Problem, no deterministic protocol can exist for an n-processor system if the number t of faulty processors is allowed to be as large as n/3. In this paper we investigate the maximum achievable agreement probability &Bgr;n,t in a model in which the faulty processors can be as devious and powerful as possible. We also discuss a restricted model with &Bgr;n,t denoting the corresponding maximum achievable probability. We will prove that: (i) for n = 3, t = 1 (the first nontrivial case), &Bgr;3,1 = (√5 - 1)/2 (the reciprocal of the golden ratio); (ii) for all &egr; with 0 t/n 1 - log (1 -&egr;)1/2/ log (1 - (1 -&egr;)1/2) then &Bgr;tn,t