三值FPRM电路极性间转换算法及其在面积优化中的应用

通过对三值FPRM(Fixed-polarity Reed-Muller)展开式和四值列表技术的研究，提出了一种三值FPRM电路极性间转换算法，并将其应用于电路面积优化.首先根据四值RM(Reed Muller)逻辑多项式系数的计算方法，推导出三值FPRM展开式极性间系数转换算法；然后利用该算法，结合三值模代数特点以及电路面积估计模型，沿非循环格雷码极性遍历路径进行三值FPRM电路面积最佳极性搜索，得到面积最优的FPRM电路.最后对8个MCNC基准电路进行测试,结果表明：与0极性Reed-Muller电路相比，三值FPRM电路的面积平均减少56.2%.

Ternary FPRM circuit conversion algorithm between polarities and its application in area optimization

Based on the research of ternary FPRM（Fixe＆polarity Reed-Muller） expansions and quaternary tabular tech- niques, a ternary FPRM circuit conversion algorithm between polarities is proposed and applied to the area optimization. Firstly, according to the calculation method of the quaternary RM（Reed-Muller） polynomial coefficients, the ternary FPRM expansion coefficients between polarities conversion algorithm is derived. Secondly, on the basis o{ this algorithm and com- bined with the characteristics of ternary modulo algebraic and the area estimation model, the best polarity of the minimum area of ternary FPRM circuits is found following the polarity traversal path of acyclic-gray code. Finally, the method was used for solving eight MCNC benchmarks, and the results show that the area of ternary FPRM circuits has achieved average saving 56.2 % in comparison with those Reed-Muller circuits under polarity 0.