Please use this identifier to cite or link to this item: https://research.matf.bg.ac.rs/handle/123456789/602
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dc.contributor.authorMarić, Filipen_US
dc.contributor.authorŽivković, Miodragen_US
dc.contributor.authorVučković, Bojanen_US
dc.date.accessioned2022-08-13T15:50:05Z-
dc.date.available2022-08-13T15:50:05Z-
dc.date.issued2012-08-17-
dc.identifier.isbn9783642313738-
dc.identifier.issn03029743en
dc.identifier.urihttps://research.matf.bg.ac.rs/handle/123456789/602-
dc.description.abstractThe Frankl's conjecture, formulated in 1979. and still open, states that in every family of sets closed for unions there is an element contained in at least half of the sets. FC-families are families for which it is proved that every union-closed family containing them satisfies the Frankl's condition (e.g., in every union-closed family that contains a one-element set a, the element a is contained in at least half of the sets, so families of the form a are the simplest FC-families). FC-families play an important role in attacking the Frankl's conjecture, since they enable significant search space pruning. We present a formalization of the computer assisted approach for proving that a family is an FC-family. Proof-by-computation paradigm is used and the proof assistant Isabelle/HOL is used both to check mathematical content, and to perform (verified) combinatorial searches on which the proofs rely. FC-families known in the literature are confirmed, and a new FC-family is discovered. © 2012 Springer-Verlag.en
dc.relation.ispartofLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)en_US
dc.titleFormalizing Frankl's conjecture: FC-familiesen_US
dc.typeConference Paperen_US
dc.relation.publicationInternational Conference on Intelligent Computer Mathematics CICM 2012en_US
dc.identifier.doi10.1007/978-3-642-31374-5_17-
dc.identifier.scopus2-s2.0-84864961101-
dc.identifier.urlhttps://api.elsevier.com/content/abstract/scopus_id/84864961101-
dc.contributor.affiliationInformatics and Computer Scienceen_US
dc.relation.firstpage248en_US
dc.relation.lastpage263en_US
dc.relation.volume7362 LNAIen_US
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.cerifentitytypePublications-
item.grantfulltextnone-
item.openairetypeConference Paper-
crisitem.author.deptInformatics and Computer Science-
crisitem.author.orcid0000-0001-7219-6960-
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