GRMIN: a heuristic simplification algorithm for generalized Reed-Muller expressions

A generalized Reed-Muller expression (GRM) is a type of AND-EXOR expressions. In a GRM, each variable may appear both complemented and uncomplemented. Networks realized using GRMs are easily tested. This paper presents GRMIN, a heuristic simplification algorithm for GRMs of multiple-output functions. GRMIN uses eight rules. As the primary objective, it reduces the number of products, and as the secondary objective, it reduces the number of literals. Experimental results show that, in most cases, GRMs require fewer products than conventional sum-of-products expressions (SOPs). GRMIN outperforms existing algorithms.