An Algorithm for multi-output Boolean logic minimization

Abstract

A new algorithm is presented for a guaranteed absolute minimal solution to the problem of Boolean Logic Minimization in its most generalized form of multi-output function with arbitrary cost criterion.

The proposed algorithm is shown to be tighter than the Quine-McCluskey method in its ability to eliminate redundant prime implicants, making it possible to simplify the cyclic tables. In its final form, the proposed algorithm is truly concurrent in generation of prime implicants and construction of minimal forms. A convenient and efficient technique is used for identifying existing prime implicants. Branch-and-bound method is employed to restrict the search tree to a cost cut-off value depending on the definition of cost function specified.

A most generalized statement of the algorithm is formulated for manual as well as computer implementation and its application is illustrated with an example. A program written in Pascal, for classical diode-gate cost function as well as PLA-area cost function, is developed and tested for an efficient computer implementation. Finally, various advantages of the proposed approach are pointed out by comparing it with the classical approach of Quine-McCluskey method.