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X-WR-CALDESC:Events for Discrete Mathematics Group
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DTSTART:20190101T000000
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DTSTART;TZID=Asia/Seoul:20200128T163000
DTEND;TZID=Asia/Seoul:20200128T173000
DTSTAMP:20260420T114904
CREATED:20191216T045747Z
LAST-MODIFIED:20240705T203007Z
UID:1940-1580229000-1580232600@dimag.ibs.re.kr
SUMMARY:Dillon Mayhew\, Courcelle's Theorem for hypergraphs
DESCRIPTION:Courcelle’s Theorem is an influential meta-theorem published in 1990. It tells us that a property of graph can be tested in polynomial time\, as long as the property can expressed in the monadic second-order logic of graphs\, and as long as the input is restricted to a class of graphs with bounded tree-width. There are several properties that are NP-complete in general\, but which can be expressed in monadic logic (3-colourability\, Hamiltonicity…)\, so Courcelle’s Theorem implies that these difficult properties can be tested in polynomial time when the structural complexity of the input is limited. \nMatroids can be considered as a special class of hypergraphs. Any finite set of vectors over a field leads to a matroid\, and such a matroid is said to be representable over that field. Hlineny produced a matroid analogue of Courcelle’s Theorem for input classes with bounded branch-width that are representable over a finite field. \nWe have now identified the structural properties of hypergraph classes that allow a proof of Hliněný’s Theorem to go through. This means that we are able to extend his theorem to several other natural classes of matroids. \nThis talk will contain an introduction to matroids\, monadic logic\, and tree-automata. \nThis is joint work with Daryl Funk\, Mike Newman\, and Geoff Whittle.
URL:https://dimag.ibs.re.kr/event/2020-01-28/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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