旋转对称逻辑公式的构造

Construction Method of Rotation Symmetric Logic Formulas

给出了n=p_1^(a1)p_2^(a2)···p_(ωn)^(aωn)时已有方法计算长圈个数错误的反例,并得到了此情况下正确的长圈个数计算公式.研究了如何构造汉明重量为某个定值的旋转对称布尔函数.将旋转对称布尔函数引入到计量逻辑学中,提出了旋转对称逻辑公式的概念.找到了如何构造真度为某个定值的旋转对称逻辑公式的方法。

A counterexample of wrongly counting the number of long cycles with the known method when n equals p 1 a1 p2 a2…pwn awn has been given. Then I have found a right way to count the number of long cycles in this case. Furthermore, how to construct a Rotation Symmetric Boolean Function where its hamming weight is constant has been studied. Rotation Symmetric Formulas has been defined after the functions introduced in the field of logic. Correspondingly, we obtain a method of how to construct a Rotation Symmetric Logic Formula where its truth degree is a constant number. Key words：Rotation Symmetric Logic Formulas ; Rotation Symmetric Boolean Functions ; Long Cycles; Hamming Weight ; Construction