Computing the minimum DNF representation of Boolean functions defined by intervals Original Research Article

For any two n-bit numbers image define the Boolean function image to be the function for which image if and only if x is the binary representation of a number in the interval image. We consider the disjunctive normal form representation of such functions, and show how to compute such a representation with a minimum number of disjuncts in linear time. We also show how to compute a minimum “disjoint” representation; i.e., a representation in which the domains of the disjuncts are mutually disjoint. The minimum disjunctive normal form can be applied to devise efficient constraint satisfaction systems for automatic generation of test patterns.