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<p><b>Abstract</b>—In a fault-tolerant distributed system, it is often necessary for nonfaulty processes to agree on the value of a shared data item. The criterion of <it>Approximate Agreement</it> does not require processes to achieve exact agreement on a value; rather, they need only agree to within a predefined numerical tolerance. Approximate Agreement can be achieved through convergent voting algorithms. Previous research has studied convergent voting algorithms under mixed-mode or <it>hybrid</it> fault models, such as the Thambidurai and Park Hybrid fault model, comprised of three fault modes: <it>asymmetric</it>, <it>symmetric</it>, and <it>benign</it>. This paper makes three major contributions to the state of the art in fault-tolerant convergent voting. 1) We partition both the asymmetric and symmetric fault modes into disjoint <it>omissive</it> and <it>transmissive</it> submodes. The resulting five-mode hybrid fault model is a superset of previous hybrid fault models. 2) We present a new family of voting algorithms, called <it>Omission Mean Subsequence Reduced</it> (OMSR), which implicitly recognize and exploit omissive behavior in malicious faults while still maintaining full Byzantine fault tolerance. 3) We show that OMSR voting algorithms are more fault-tolerant than previous voting algorithms if any of the currently active faults is omissive.</p>
Approximate agreement, clock synchronization, convergent voting algorithms, fault-tolerant distributed systems, hybrid faults.

R. Kieckhafer and M. Azadmanesh, "Exploiting Omissive Faults in Synchronous Approximate Agreement," in IEEE Transactions on Computers, vol. 49, no. , pp. 1031-1042, 2000.
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