本文证明了任意一元布尔方程(任意个已知变元)均可用已知变元的换元法化为至多含两个已知变元的一元布尔方程
并给出了解和解存在的充要条件的一般表示式;由此得到的计算程序常可大大减少计算量.由此结果
并利用提出的降维法
对多元布尔方程亦可得到相应的计算程序.对某些未知变元个数为无穷的布尔方程
应用上述结果亦可得到解.
In[1] the method of truth table to solve Boolean equations was presented.But by that method the calculation quantity is huge. This article proved thatany Boolean equation of one unknown may be transformed into that of at mosttwo knowns by means of the change of known variables and obtained its generalsolution. The necessary and sufficient condition for existence of solution is alsoobtained. In the case of multi-unknowns and some equations of enumerableinfinite number of unknowns this method is also effective.
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