Incremental polynomial time dualization of quadratic functions and a subclass of degree‐k functions

We consider the problem of dualizing a Boolean function f represented by a DNF. In its most general form, this problem is commonly believed not to be solvable by a quasi‐polynomial total time algorithm. We show that if the input DNF is quadratic or is a special degree‐k DNF, then dualization turns out to be equivalent to hypergraph dualization in hypergraphs of bounded degree and hence it can be achieved in incremental polynomial time.