Browsing by Subject "Dualization"

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    Boolean normal forms, shellability, and reliability computations
    (Society for Industrial and Applied Mathematics, 2000) Borgs, E.; Crama, Y.; Ekin, O.; Hammer, P.L.; Ibaraki, T.; Kogan, A.
    Orthogonal forms of positive Boolean functions play an important role in reliability theory, since the probability that they take value 1 can be easily computed. However, few classes of disjunctive normal forms are known for which orthogonalization can be efficiently performed. An interesting class with this property is the class of shellable disjunctive normal forms (DNFs). In this paper, we present some new results about shellability. We establish that every positive Boolean function can be represented by a shellable DNF, we propose a polynomial procedure to compute the dual of a shellable DNF, and we prove that testing the so-called lexico-exchange (LE) property (a strengthening of shellability) is NP-complete.
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    Incremental polynomial time dualization of quadratic functions and a subclass of degree-k functions
    (Springer, 2011-08) Karaşan, O. E.
    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.