Synchronous Condition-Based Consensus Adapting to Input-Vector Legality

Abstract

This paper proposes a novel condition-based algorithm for the uniform consensus in synchronous systems. The proposed algorithm is adaptive in the sense that its execution time depends on actual difficulty of input vectors, legality level, which is newly formalized in this paper. On the assumption that majority of processes are correct, the algorithm terminates within min {f + 2 − − l, t + 1} rounds if l < f, where f and t is the actual and the maximum numbers of faults respectively, and l is the legality level of input vectors. Moreover, the algorithm terminates in 1 round if l ≥ t and f=0, and terminates within 2 rounds if l ≥ f holds. Compared with previous algorithms, for the case of t < n/2, the algorithm achieves the best time complexity in almost all situations.