Browsing by Subject "Boolean function"

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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.
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    On connected Boolean functions
    (Elsevier, 1999) Ekin, Oya; Hammer, P. L.; Kogan, A.
    A Boolean function is called (co-)connected if the subgraph of the Boolean hypercube induced by its (false) true points is connected; it is called strongly connected if it is both connected and co-connected. The concept of (co-)geodetic Boolean functions is de ned in a similar way by requiring that at least one of the shortest paths connecting two (false) true points should consist only of (false) true points. This concept is further strengthened to that of convexity where every shortest path connecting two points of the same kind should consist of points of the same kind. This paper studies the relationships between these properties and the DNF representations of the associated Boolean functions. ? 1999 Elsevier Science B.V. All rights reserved.