Algebraic properties of faults in logic networks : Stanford Univ. Electronics Labs. F. W. Clegg, E. J. McCluskey. March (1970), 149 pp. (1093–7102) P-170364, SU-SEL-69–078. NONR-225-83-NR-373-360 TR-4

Abstract

Abstract : The work describes a general study of the effects of so-called 'stuck-at' faults on the structural and functional characteristics of combinational logic networks. It is shown that some of the possible faults which can occur in a given network bear relations to certain other possible faults in that network. Knowledge of these relations greatly facilitates consideration of networks in the presence of failures. The two types of relations considered are those of covering and equivalence. The covering relations introduced reflect the mechanisms whereby the presence of certain faults in a network renders the occurrence of other failures to some extent unobservable. The equivalence relations which are presented reflect the varying degrees which distinct faults in a network can be indistinguishable. A modelling technique is presented whereby the structure of a given network is represented by a labelled, directed graph. The effects of faults on this structure are modelled by appropriate transformations applied to this graph. These models and the associated algebraic techniques which are developed provide a particularly convenient means of characterizing the relations between, and other aspects of, the faults which can occur in a network. Key theorems establish necessary and sufficient conditions for the existence of the various covering and equivalence relations which permit one to determine these relations directly from a systematic inspection the network under study. (Author)