Abstract: 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.

Key words: monotone decomposition, boolean funcition on B₂, quasi-monotone decomposition