Irredundant Normal Forms and Minimal Dependence Sets of a Boolean Function

A new method is presented for determining all minimal dependence sets, irredundant normal forms, and irredundant normal forms of minimal dependence sets of a Boolean function f. The method reduces the above problems into those of determining all minimal positive dependence sets, irredundant positive normal forms, and irredundant positive normal forms of minimal positive dependence sets, respectively, of a Boolean function f* corresponding to f. For each problem a corresponding cover formula is developed such that the prime implicants of it are in one-to-one correspondence to all possible solutions.