Boolean Normal Forms, Shellability, And Reliability Computations

. 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 e#ciently 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. Ke words. Boolean functions, orthogonal DNFs, dualization, shellability, reliability AMS sub je classifications. Primary, 90B25; Secondary, 05C65, 68R05 PII. S089548019732180X 1. Introduction. A classicalprobic of Boolean theory is to derive an orthogonal form, or disjoint pr..

7th International Meshing Roundtable '98

The goal of the 7th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the past, the Roundtable has enjoyed significant participation from each of these groups from a wide variety of countries

College of Arts and Sciences

Cornell University Courses of Study Vol. 91 1999/200