Optimally simulating crash failures in a byzantine environment

The difficulty of designing of fault-tolerant distributed algorithms increases with the severity of failures that an algorithm must tolerate. Researchers have simplified this task by developing methods that automatically translate protocols tolerant of “benign” failures into ones tolerant of more “severe” failures. In addition to simplifying the design task, these translations can provide insight into the relative impact of different models of faulty behavior on the ability to provide fault-tolerant applications. Such insights can be gained by examining the properties of the translations. The roundcomplexity of a translation is such a property; it is the number of rounds of communication that the translation uses to simulate one round of the original algorithm. This paper considers synchronous systems and examines the problem of developing translations from simple stopping (crash) failures to completely arbitrary behavior with round-complexities 2, 3, and 4, respectively. In each case, we show a lower bound on the number of processors that must remain correct. We show matching upper bounds for all of these by developing three new translation techniques that are each optimal in the number of processors required. These results fully characterize the optimal translations between crash and arbitrary failures.