A characterization of eventual Byzantine agreement

We investigate eventual Byzantine agreement (EBA) in the crash and omission failure modes. The emphasis is on characterizing optimal EBA protocols in terms of the states of knowledge required by the processors in order to attain EBA. It is well known that common knowledge among the nonfaulty processors is a necessary and sufficient condition for attaining simultaneous Byzantine agreement (SBA). We define a new variant that we call continual common knowledge and use it to provide necessary and sufficient conditions for attaining EBA. Using this characterization, we provide a technique that allows us to start with any EBA protocol and convert it to an optimal EBA protocol using a two-step process.