多處理機系統之(t,k)偵錯

Abstract

System-level diagnosis is a process of identifying faulty processors in a system by conducting tests on various processors and interpreting the test results. The application of system-level diagnosis is the diagnosis of multiprocessor systems. There are five important issues in system-level diagnosis: diagnosis model, diagnosis strategy, diagnosis algorithm, fault model and diagnosability. We focus the (t,k)-diagnosis strategy, (t,k)-diagnosis algorithm, random fault model and (t,k)-diagnosis diagnosability for some multiprocessor systems under the PMC and MM* models. (t,k)-diagnosis, which is a generalization of sequential diagnosis, requires at least k faulty processors identified and replaced in each iteration provided there are at most t faulty processors, where t >= k. In this thesis, faulty nodes of multiprocessor systems may occur everywhere without any restriction. We propose a unified approach to compute the (t,k)-diagnosability for numerous multiprocessor systems, including hypercubes, crossed cubes, twisted cubes, locally twisted cubes, multiply twisted cubes, generalized twisted cubes, recursive circulants, Mobius cubes, Mcubes, star graphs, bubble-sort graphs, pancake graphs, and burnt pancake graphs. The key concept of our approach is to sketch the common graph properties of the above multiprocessor systems and demonstrate that their underlying topologies have a common super class of graphs, called component-composition graphs. We then show that the m-dimensional component-composition graph G for m >= 4 is a lower bound of the (t,k)-diagnosability. Based on this result, the (t,k)-diagnosability of the referred multiprocessor systems can be efficiently computed.