Doubly-expedited one-step Byzantine consensus

It is known that Byzantine consensus algorithms guarantee one-step decision only in favorable situations (e.g. when all processes propose the same value) and no one-step algorithm can support two-step decision. This paper presents DEX, a novel one-step Byzantine algorithm that circumvents these impossibilities using the condition-based approach. Algorithm DEX has two distinguished features: Adaptiveness and Double-expedition property. Adaptiveness makes it sensitive to only actual number of failures so that it provides fast termination for more number of inputs when there are fewer failures (a common case in practice). The double-expedition property facilitates two-step decision in addition to one-step decision by running two condition-based mechanisms in parallel. To the best of our knowledge, double-expedition property is the new concept introduced by this paper, and DEX is the first algorithm having such a feature. Although DEX takes four steps at worst in well-behaved runs while existing one-step algorithms take only three, it is expected to work efficiently because the worst-case does not occur so often in practice.