Abstract
the paper describes a method for combinational logical synthesis using a ternary polarity conversion technique (TPCT) and the Reed-Muller form over GF(3). A new algorithm is presented that allows us to obtain the ternary fixed polarity Reed-Muller (FPRM) expansion. The popular polarity conversion over GF(3) is obtained by the coefficient matrix technology. This paper presents a non-matrix operation method for FPRM expansion. The new method allows us to build the FPRM form based on the calculation of FPRM coefficients, and then an exhaustive-search optimization algorithm based on Gray Code is developed to find the optimum ternary FPRM expansion. We use the method in the reported paper to generate ternary test functions from the MCNC benchmarks circuits. The algorithm is tested on fifteen functions and the experimental results are shown in this paper.
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