Computational Aspects of Monotone Dualization

Dualization of a monotone Boolean function represented by a conjunctive normal form (CNF) is a problem which, in different disguise, is ubiquitous in many areas including computer science, artificial intelligence, data mining, maching learning, and game theory to mention some of them. It is also one of the few problems whose precise tractability status (in terms of polynomial-time solvability) is still unknown, and now open for more than 30 years. We briefly survey computational results for this problem, which includes the remarkable result by Fredman and Khachiyan that the problem is solvable in quasi-polynomial time (and thus most likely not coNP-hard), as well as on follow-up works.