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This paper is a study of switching functions realizable by a single cascaded switching network composed of two-input, one-output elements where a distinct variable is applied to one input and the other receives the output of the previous element. A special type of Boolean formula called a standard cascade form is introduced with the property that all cascade realizable functions, and only these, can be written in this form. This characterization leads to a strong necessary condition on such functions: there is no consensus for any pair of its prime implicants which are, therefore, all core. It also leads to a new, efficient procedure for testing an arbitrary function f for cascade realizability. The test operates on the prime implicants of f, and yields a realization employing a particular complete set of cell types from which it is especially easy to derive any other realization using any other complete set.
Arrays of cascades, Boolean formula, cascaded switching networks, core prime implicants, optimal realization, prime implicants, standard cascade form, switching functions, two-input one-output elements.
C.D. Weiss, "The Characterization and Properties of Cascade Realizable Switching Functions", IEEE Transactions on Computers, vol. 18, no. , pp. 624-633, July 1969, doi:10.1109/T-C.1969.222729
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