The Computational Complexity of a Class of Minimization Algorithms for Switching Functions

Most minimization algorithms produce an irredundant sum of products by first generating all prime implicants of a switching function. In this note we show that such an approach can be a wasteful one for an already complex problem. Specifically we show that there are functions for which the useful prime implicants form an extremely small fraction of all prime implicants, where we define a prime implicant to be useful if there is at least one irredundant sum of products which includes it.