Generalized Inclusive Forms — New Canonical Reed-Muller Forms Including Minimum ESOPs

Reed-Muller (AND/EXOR) expansions play an important role in logic synthesis and circuit design by producing economical and highly-testable implementations of Boolean functions [3–6]. The range of Reed-Muller expansions include canonical forms, i.e. expansions that create unique representations of a Boolean function. Several large families of canonical forms: fixed polarity Reed-Muller forms (FPRMs), generalized Reed-Muller forms (GRMs), Kronecker forms (KROs), and pseudo- Kronecker forms (PKROs), referred to as the Green/Sasao hierarchy, have been described [7–9]. (See Fig. 1 for a settheoretic relationship between these families.