On the complexity of mod-2l sum PLA's

Consideration is given to the realization of logic functions by using PLAs with an exclusive-OR (EXOR) array, where a function is represented by mod-2 (EXOR) sum-of-products (ESOPs) and both true and complemented variables are used. The authors propose a new PLA structure using an EXOR array. They derive upper bounds on the number of products of this type of PLA that are useful for estimating the size of a PLA as well as for assessing the minimality of the solutions obtained by heuristic ESOP minimization algorithms. Computer simulation using randomly generated functions shows that PLAs with the EXOR array require, on the average, fewer products than conventional PLAs. For symmetric functions, the authors conjecture that the PLAs with an EXOR array require, at most, as many products as the conventional PLAs. The proposed PLAs can be made easily testable by adding a small amount of hardware.>