## Algebraic Properties of Faults in Logic NetworksDepartment of Electrical Engineering, Stanford University., 1970 - Logic, Symbolic and mathematical - 140 pages 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). |

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### Contents

INTRODUCTION | 1 |

FAULTS AND THEIR EFFECTS | 22 |

k TWO MODELS OF THE EFFECTS OF STUCKAT FAULTS | 30 |

2 other sections not shown

### Common terms and phrases

application bias vertices Boolean function components of F concatenation congruence relation covering relations defined design network design structure directed graph edges incident electronic circuits example exists F and F failures fault bias vertex fault components fault F fault function faulty network functional equivalence classes given network graph G graph of Fig graph theory idempotence Kl K2 lence Let F logic networks logical constant logical schematic logical value model G multiple fault NAND necessary and sufficient network containing network output function network structure network whose logical number of classes output vertex possible stuck-at faults presence of F primary logical model prime implicants R-structural R-structural equivalence classes R-Transformation reconvergent fanout paths reduced logical model relations between faults schematic diagram Schertz set of components shown in Fig signal single faults structural equivalence sufficient conditions switching circuit switching network techniques Theorem 6.1 Transformation vertices in G