Lower Bounds for Achieving Synchronous Early Stopping Consensus with Orderly Crash Failures

In this paper, we discuss the consensus problem for synchronous distributed systems with orderly crash failures. For a synchronous distributed system of n processes with up to t crash failures and f failures actually occur, first, we present a bivalency argument proof to solve the open problem of proving the lower bound, min (t + 1, f + 2) rounds, for early-stopping synchronous consensus with orderly crash failures, where t < n - 1. Then, we extend the system model with orderly crash failures to a new model in which a process is allowed to send multiple messages to the same destination process in a round and the failing processes still respect the order specified by the protocol in sending messages. For this new model, we present a uniform consensus protocol, in which all non-faulty processes always decide and stop immediately by the end of f + 1 rounds. We prove that the lower bound of early stopping protocols for both consensus and uniform consensus are f + 1 rounds under the new model, and our proposed protocol is optimal.

Specialization of Perceptual Processes

In this report, I discuss the use of vision to support concrete, everyday activity. I will argue that a variety of interesting tasks can be solved using simple and inexpensive vision systems. I will provide a number of working examples in the form of a state-of-the-art mobile robot, Polly, which uses vision to give primitive tours of the seventh floor of the MIT AI Laboratory. By current standards, the robot has a broad behavioral repertoire and is both simple and inexpensive (the complete robot was built for less than $20,000 using commercial board-level components). The approach I will use will be to treat the structure of the agent's activity---its task and environment---as positive resources for the vision system designer. By performing a careful analysis of task and environment, the designer can determine a broad space of mechanisms which can perform the desired activity. My principal thesis is that for a broad range of activities, the space of applicable mechanisms will be broad enough to include a number mechanisms which are simple and economical. The simplest mechanisms that solve a given problem will typically be quite specialized to that problem. One thus worries that building simple vision systems will be require a great deal of {it ad-hoc} engineering that cannot be transferred to other problems. My second thesis is that specialized systems can be analyzed and understood in a principled manner, one that allows general lessons to be extracted from specialized systems. I will present a general approach to analyzing specialization through the use of transformations that provably improve performance. By demonstrating a sequence of transformations that derive a specialized system from a more general one, we can summarize the specialization of the former in a compact form that makes explicit the additional assumptions that it makes about its environment. The summary can be used to predict the performance of the system in novel environments. Individual transformations can be recycled in the design of future systems.