Evaluation of -valued Fixed Polarity Generalizations of Reed-Muller Canonical Form

This paper compares the complexity of three different fixed polarity generalizations of Reed-Muller canonical form to multiple-valued logic: the Galois Field-based expansion introduced by Green and Taylor, the Reed-MullerFourier form of Stanković and Moraga, and the expansion over addition modulo , minimum and the set of all literal operators introduced by the author and Muzio. An algorithm for computing the minimal canonical forms for these generalizations is implemented and applied to a set of encoded 4-valued benchmark functions, 3and 4-valued adders and multipliers. The experimental results show that, for the benchmark functions, the Reed-Muller-Fourier form and our expansion yield a comparable number of products on average. They have 40% less products on average than the expansion of Green and Taylor. The Reed-MullerFourier form gives a compact representation for adders, while our expansion seems to be suitable for multipliers.