IEEE Transactions on Computers · 1975 · 435 citations · 5 references
Natural SciencesComputer ScienceMathematicsAlgorithmsFault-tolerant ComputingProbability TheoryBoolean AlgebraBoolean Network ModelsCombinational Logic DescriptionConditional ProbabilityFault DetectionFault DiagnosisBoolean Function RepresentationCombinational Logic DesignProbabilistic AnalysisProbabilistic Boolean NetworksProbabilistic Fault ModelingProbabilistic Logic
The authors present two methods for computing the probability that a general combinational network outputs 1 given the probabilities of its inputs being 1. They define signal probability and independence, prove how Boolean operations translate to algebraic operations on probabilities, and illustrate the results with a fault‑detection test‑generation example. These results yield two simple algorithms for calculating output probabilities.
In this correspondence two methods are given for calculating the probability that the output of a general combinational network is 1 given the probabilities for each input being 1. We define the notions of the probability of a signal and signal independence. Then several proofs are given to show the relationship between Boolean operations and algebraic operations upon probabilities. As a result of these, two simple algorithms are presented for calculating output probabilities. An example of the usefulness of these results is given with respect to the generation of tests for the purpose of fault detection.
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Probability, Random Variables, and Stochastic Processes
Irwin Miller · Technometrics · 1966 · 2K citations
Engineering, Mathematics, Physics +14
Sergio T. Ribeiro · IEEE Transactions on Electronic Computers · 1967 · 82 citations