This paper studies the impact of omission failures on asynchronous distributed systems with crash-stop failures. We provide two different transformations for algorithms, failure detectors, and problem specifications, one of which is weakest failure detector preserving. We prove that our transformation of failure detector Ω [1] is the weakest failure detector for consensus in environments with crash-stop and permanent omission failures and a majority of correct processes. Our results help to use the power of the well-understood crash-stop model to automatically derive solutions for the general omission model, which has recently raised interest for being noticeably applicable for security problems in distributed environments equipped with security modules such as smartcards [2,3,4].
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