Exploiting omissive faults in synchronous approximate agreement

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 Approximate Agreement 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 hybrid fault models, such as the Thambidurai and Park Hybrid fault model, comprised of three fault modes: asymmetric, symmetric, and benign. 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 omissive and transmissive 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 Omission Mean Subsequence Reduced (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.