Resiliency of interactive distributed tasks

Interaction is a fundamental notion in computation. In many cases, important properties are revealed by considering the interactive aspects of problems. In this work, we examine the power and limitations of interaction in the context of fault-tolerant, asynchronous distributed computing. We focus on two models of interprocess communication - shared memory, and message passing. Interactive distributed tasks naturally occur in many distributed systems. In such a task, each of n processors receives a local input, responds with some local output, then receives a second input (possibly depending on the response), responds to i t, and so on. Different processors can be at different stages simultaneously, so that additional inputs are received by fast processors while slow processors are still working on early inputs. Interactive distributed tasks have strong expressive power. They include, for example, both decision tasks and sequential systems as special cases. The main result of this work is an exact characterization of the interactive tasks which can be solved by randomized t-resilient protocols. The major tool we use in the characterization is a directed acyclic graph that is associated with an interactive task. Properties of this graph are used to determine the resiliency of the task, and to devise a "generic" resilient algorithm which solves such tasks.