Boolean normal forms, shellability, and reliability computations

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dc.citation.epage226en_US
dc.citation.issueNumber2en_US
dc.citation.spage212en_US
dc.citation.volumeNumber13en_US
dc.contributor.authorBorgs, E.en_US
dc.contributor.authorCrama, Y.en_US
dc.contributor.authorEkin, O.en_US
dc.contributor.authorHammer, P.L.en_US
dc.contributor.authorIbaraki, T.en_US
dc.contributor.authorKogan, A.en_US
dc.date.accessioned2016-02-08T10:38:35Z
dc.date.available2016-02-08T10:38:35Z
dc.date.issued2000en_US
dc.departmentDepartment of Industrial Engineeringen_US
dc.description.abstractOrthogonal 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.en_US
dc.identifier.doi10.1137/S089548019732180Xen_US
dc.identifier.issn0895-4801
dc.identifier.urihttp://hdl.handle.net/11693/25061
dc.language.isoEnglishen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.isversionofhttps://doi.org/10.1137/S089548019732180Xen_US
dc.source.titleSIAM Journal on Discrete Mathematicsen_US
dc.subjectBoolean functionsen_US
dc.subjectDualizationen_US
dc.subjectOrthogonal DNFsen_US
dc.subjectReliabilityen_US
dc.subjectShellabilityen_US
dc.titleBoolean normal forms, shellability, and reliability computationsen_US
dc.typeArticleen_US
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