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In 1982, Lamport et al. presented the so-called Byzantine generals problem as follows: a group of generals of the Byzantine army camped with their troops around an enemy city. Communicating only by messenger, the generals must agree upon a common battle plan. However, one or more of them may be traitors who will try to confuse the others. The problem is to find an algorithm to ensure that the loyal generals will reach agreement. The authors gave a sharp characterization of the power of the Byzantine generals. It was shown that if the fraction of Byzantine generals is less than 1/3, there is a way for the loyal generals to reach a consensus agreement, regardless of what the Byzantine generals do. If the fraction is above 1/3, consensus can no longer be guaranteed. This article examines the Byzantine generals problem in the context of distributed inference, where data collected from remote locations are sent to a fusion center (FC) for processing and inference. The assumption is that the data are potentially tampered or falsified by some internal adversary who has the knowledge about the algorithm used at the FC. We refer to the problem considered as distributed inference with Byzantine data.