Tight bounds for shared memory systems accessed by byzantine processes

We provide efficient constructions and tight bounds for shared memory systems accessed by n processes, up to t of which may exhibit Byzantine faults, in a model previously explored by Malkhi et al. [MMRT00]. We show that sticky bits are universal in the Byzantine failure model for n ≥ 3t + 1, an improvement over the previous result requiring n ≥ (2t+1)(t+1). Our result follows from a new strong consensus construction that uses sticky bits and tolerates t Byzantine failures among n processes for any n ≥ 3t + 1, the best possible bound on n for strong consensus. We also present tight bounds on the efficiency of implementations of strong consensus objects from sticky bits and similar primitive objects.