A Graph Theoretic Approach to Fault Tolerant Computing.

Abstract

Abstract : This report describes the results of an initial effort to identify properties of labelled graphs which are useful for the representation and analysis of fault tolerant digital systems. It builds on the results of previous work, where the feasibility of using LOGOS and Petri Nets to represent fault tolerant systems was assessed. The properties of conventional directed graphs were reviewed to identify any properties relevant to fault tolerance. Concepts such as balanced graphs, strongly connected graphs, cut sets, circuits, and reachability were identified as useful and shown to be applicable to labelled graphs. Next the fault phenomena commonly seen in digital systems were classified, both from the viewpoint of their observable effects on the faulty system and from the more conventional viewpoint of their sources. Six functional Fault Classes were defined which accurately describe virtually all the common control related fault phenomena. The existing labelled graph theory was then examined for properties related to the Functional Fault Classes. Concepts such as liveness, boundedness, siphons, traps, and invariants among others were identified as useful. A taxonomy of structural and dynamic properties useful for fault tolerant analysis is given. The relationship between these properties and their application to fault tolerant system analysis is described. Finally, limitations of this approach and directions for future work are described. (Author)