Boolean functions with long prime implicants

Ondřej Čepek, Petr Kučera, Stanislav Kuřík
2013 Information Processing Letters  
In this short note we introduce a class of Boolean functions defined by a minimum length of its prime implicants. We show that given a DNF one can test in polynomial time whether it represents a function from this class. Moreover, in case that the answer is affirmative we present a polynomial time algorithm which outputs a shortest DNF representation of the given function. Therefore the defined class of functions is a new member of a relatively small family of classes for which the Boolean
more » ... ization problem can be solved in polynomial time. Finally, we present a generalization of the above class which is still recognizable in polynomial time, and for which the Boolean minimization problem can be approximated within a constatnt factor.
doi:10.1016/j.ipl.2013.07.001 fatcat:jep3g5m4rnhk3lvdwei44w7aoi