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dc.contributor.authorSezener, Can Eren
dc.contributor.authorÖztop, Erhan
dc.date.accessioned2015-10-30T12:37:34Z
dc.date.available2015-10-30T12:37:34Z
dc.date.issued2015-08
dc.identifier.issn1530-888X
dc.identifier.urihttp://www.mitpressjournals.org/doi/abs/10.1162/NECO_a_00750#.VjNrtbfhDIU
dc.identifier.urihttp://hdl.handle.net/10679/1001
dc.descriptionDue to copyright restrictions, the access to the full text of this article is only available via subscription.
dc.description.abstractBoolean functions (BFs) are central in many fields of engineering and mathematics, such as cryptography, circuit design, and combinatorics. Moreover, they provide a simple framework for studying neural computation mechanisms of the brain. Many representation schemes for BFs exist to satisfy the needs of the domain they are used in. In neural computation, it is of interest to know how many input lines a neuron would need to represent a given BF. A common BF representation to study this is the so-called polynomial sign representation where and 1 are associated with true and false, respectively. The polynomial is treated as a real-valued function and evaluated at its parameters, and the sign of the polynomial is then taken as the function value. The number of input lines for the modeled neuron is exactly the number of terms in the polynomial. This letter investigates the minimum number of terms, that is, the minimum threshold density, that is sufficient to represent a given BF and more generally aims to find the maximum over this quantity for all BFs in a given dimension. With this work, for the first time exact results for four- and five-variable BFs are obtained, and strong bounds for six-variable BFs are derived. In addition, some connections between the sign representation framework and bent functions are derived, which are generally studied for their desirable cryptographic properties.en_US
dc.language.isoengen_US
dc.publisherMIT Pressen_US
dc.rightsrestrictedAccess
dc.titleMinimal sign representation of boolean functions: algorithms and exact results for low dimensionsen_US
dc.typeArticleen_US
dc.peerreviewedyesen_US
dc.publicationstatuspublisheden_US
dc.contributor.departmentÖzyeğin University
dc.contributor.authorID(ORCID 0000-0002-3051-6038 & YÖK ID 45227) Öztop, Erhan
dc.contributor.ozuauthorÖztop, Erhan
dc.identifier.volume27
dc.identifier.issue8
dc.identifier.startpage1796
dc.identifier.endpage1823
dc.identifier.wosWOS:000360092200009
dc.identifier.doi10.1162/NECO_a_00750
dc.subject.keywordsOrder neural-networksen_US
dc.subject.keywordsPolynomial threshold functionsen_US
dc.subject.keywordsReed-muller codeen_US
dc.subject.keywordsClassificationen_US
dc.subject.keywordsCosetsen_US
dc.identifier.scopusSCOPUS:2-s2.0-84937501146
dc.contributor.ozugradstudentSezener, Can Eren
dc.contributor.authorMale2


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