Aiming at the problem of equivalent conversion from conjunctive normal form to disjunctive normal form, an effective algorithm was proposed to construct reduction tree based on discernibility matrix.

With respect to the principal disjunctive normal form and the principal conjunctive normal form, we also approach the properties of the subscript sets derived from the minimum term and maximum term.

An new concept of saturated conjunctive normal form is introduced and the nature of sat problem is studied for utilizing the characteristic of saturated conjunctive normal form.