B2上布尔函数的拟单调分解

系统地讨论了B₂上布尔函数的拟单调分解.先使用拟单调分解树来定义布尔函数拟单调分解的一般形式,使其在应用中具有很大的灵活性.然后对⊚、⊕、∪和°运算给出几种实用的拟单调分解法.最后将上述结果推广到布尔函数拟单调分解的一般形式,给出一个布尔函数可以分解成k个单调函数的逻辑组合的充分必要条件.

Quasi-monotone Decomposition of Boolean Functions on B2

In this paper, quasi-monotone decomposition of Boolean functions on B 2 is discussed systematically. The quasi-monotone decomposition tree is used to define the general form of quasi-monotone decomposition. It gives great flexibility in its application. Several practical quasimonotone decomposition approaches for boolean operators ⊚,⊕, ∪ and ° are given. Then the above results are extended to the general form of quasi-monotone decomposition. In conclusion, we give the necessary and sufficient condition under which a boolean function can be decomposed into k monotonous boolean functions.