Some Studies on Connected Cover Term Matrices of Switching Functions†

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Abstract
The central idea developed in the present paper involves the decomposition of the prime irnplicant covering problems of switching functions into the number of readily tractable sub-problems. It is shown that the minimizing function (Boolean representation of the prime implicant table) of a switching function can suitably be split up into a number of sub-functions such that the sum terms of each of these sub-functions can be arranged in any of the four possible distinct matrices called connected cover term matrices. The irredundant solutions of the sub-problem corresponding to each of the connected cover term matrices can be readily obtained, without the generation of a single redundant or duplicate solution, by following a systematic procedure suggested in the paper. The paper is concerned with the detailed study of the properties of the connected cover term matrices.

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