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.

The Japanese Business System: Key Features and Prospects for Change

This paper argues that the Japanese business system cannot be adequately understood without extending the focus of analysis beyond the individual firm to the vertical keiretsu, or business group. The vertical group or keiretsu structure was first identified and studied in the auto and electronics industries, where it is most strongly marked, but it characterizes virtually all sectors, service industries as well as manufacturing. Large industrial vertical keiretsu are composed of subsidiaries engaged in three distinct types of activities (manufacturing, marketing, and quasirelated business). The coordination and control systems are built on the flows of products, financial resources, information and technology, and people across formal company boundaries, with the parent firm controlling the key flows. The paper examines the prevailing explanations first for the emergence and then for the persistence of the vertical group structure, and looks at the current pressures for change and adaptation in the system.