UNIFIED APPROACH TO SYNCHRONOUS AND ASYNCHRONOUS APPROXIMATE AGREEMENT IN THE PRESENCE OF HYBRID FAULTS

An important problem in fault-tolerant distributed systems is maintaining agreement between non-faulty processes in the presence of undiagnosed faults. Approximate agreement defines a condition in which it is not necessary for the agreed values to be numerically identical. Rather, processes need only agree with each other to within a predefined numerical tolerance. Convergent voting algorithms which achieve Approximate Agreement have been studied in the context of two classes of systems, Synchronous & Asynchronous. Studies have also addressed both Completely Connected and partially connected systems. Together, the two properties of synchrony & connectivity yield 4 different voting domains. In all studies to date, each voting domain has been treated as a separate problem. This paper: Shows that for at least one broad family of voting algorithms, the 4 domains are special cases of a more general convergent voting problem Analyzes convergent voting under the 3-mode hybrid fault model of Thambidurai & Park. Presents a set of unifying relations applicable to all 4 voting domains. These relations are used to specify voting algorithms which optimize fault-tolerance, convergence rate, or computational overhead in any given voting domain. The task of designing a voting algorithm for a particular fault-tolerant system is thus greatly simplified.