An algorithm for the multi-level minimization of Reed-Muller representations

Abstract

There is interest currently in using Reed-Muller equations as a way of representing and manipulating switching functions, and as a means of designing circuits based on exclusive-OR gates. There are only two-level Reed-Muller minimizers in use, although the need for a multi-level minimizer has been identified. A procedure for multi-level Reed-Muller minimization has been developed. It introduces a Reed-Muller factored form and uses algebraic algorithms for factorization decomposition, resubstitution, collapsing, and extraction of common cubes and sub-expressions. The procedure has been implemented in C as a series of packages which have been added to MISII, and benchmark comparisons with minimal two-level representations are favorable.<>