This paper develops an algebra of Boolean functions that can be used to minimize a given Boolean function of several variables. The consequence of interest is that an absolute minimum can often be found faster using the new minimization procedures given in this paper than using the near-minimum found by well-known programs such as MINI and ESPRESSO that use heuristics to guide their search. The results are therefore not only of theoretical interest but also of potential use in the form of a new PLA (programmable logic array) -minimization program. Simulation results are presented in the paper to show the comparative performance of the new algorithms.

While the results of the newly developed procedures are excellent, the procedures themselves rest on several fairly involved new concepts that the authors introduce. It is hard for the reader to keep in mind the large number of new terms defined, making it necessary to often search backwards through a densely written paper. In addition, the paper is crammed full of ideas, making it hard to read, in spite of several well-chosen examples that have been worked out at appropriate junctures in the text.