Abstract
This research is in the area of multivalued combinational networks. It studies various properties of multivalued algebra and the refinement of the methods reported so far for minimizing completely and/or partially specified multivalued combinational networks.In order to analyze multivalued combinational networks, differential operators are defined. Analytical and graphical methods for computing these operators are developed. The associated properties of these operators are obtained and several theorems are proved.One application of the new multivalued differential operators is in fault detection in multivalued logic networks. An algorithm for generating a complete test set for the detection of a single stuck-at-fault is presented.The transition calculus is a powerful tool that is useful when dealing with the effect of input changes on multivalued logic networks. Using the differential operators, a multivalued differential expression matrix is defined. It is shown how a differential expression matrix can be used to provide an effective method for describing how the value of a switching function is affected by changes in its variables. Given such a differential expression matrix, determining whether a function can be found which realizes the changes in the matrix and finding such a function if it exists, leads to the development of multivalued integral calculus. Towards this end, various integrals are defined, their properties defined, and different ways of computing them are shown.The concepts of a compatible integral and the exact integral are presented and a necessary and sufficient condition is established for a given differential expression matrix to be compatibly integrable. When the latter is compatibly integrable, a method is proposed for finding the entire set of compatible integrals of the differential expression matrix.