How to Catch the Golden Fish of Minimum ESOP Into the Net of Canonical Forms

This paper describes a family of canonical Reed-Muller forms, called Inclusive Forms, which allows to represent all minimum ESOPs for any boolean function. We outline the hierarchy of known canonical forms, in particular, PseudoGeneralized Kronecker Forms [1, 2], which led us to the discovery of the new family. Next we introduce special binary trees, called S/D trees, which underlie Inclusive Forms and permit their enumeration. We show how to generate IFs and Generalized IFs. Finally, we present the results of computer experiments, which show that Inclusive Forms reduce the search space for minimum ESOP by several orders of magnitude, and this reduction grows exponentially with the number of variables.