A Sufficient Condition for Gaining Belief in Byzantine Fault-Tolerant Distributed Systems

Existing protocols for byzantine fault tolerant distributed systems usually rely on the correct agents' ability to detect faulty agents and/or to detect the occurrence of some event or action occurring on some correct agent. In this paper, we provide sufficient conditions that allow an agent to infer the appropriate beliefs from its history, and a procedure that allows these conditions to be checked in finite time. Our results thus provide essential stepping stones for developing efficient protocols and proving them correct.