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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20210101T000000
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DTSTART;TZID=Asia/Seoul:20221206T163000
DTEND;TZID=Asia/Seoul:20221206T173000
DTSTAMP:20260419T190544
CREATED:20220908T152618Z
LAST-MODIFIED:20240707T074218Z
UID:6153-1670344200-1670347800@dimag.ibs.re.kr
SUMMARY:Giannos Stamoulis\, Model-Checking for First-Order Logic with Disjoint Paths Predicates in Proper Minor-Closed Graph Classes
DESCRIPTION:The disjoint paths logic\, FOL+DP\,  is an extension of First Order Logic (FOL) with the extra atomic predicate $\mathsf{dp}_k(x_1\,y_1\,\ldots\,x_k\,y_k)\,$ expressing the existence of internally vertex-disjoint paths between $x_i$ and $y_i\,$ for $i\in \{1\,\ldots\, k\}$. This logic can express a wide variety of problems that escape the expressibility potential of FOL. We prove that for every minor-closed graph class\, model-checking for FOL+DP can be done in quadratic time. We also introduce an extension of FOL+DP\, namely the scattered disjoint paths logic\, FOL+SDP\, where we further consider the atomic predicate $\mathsf{s-sdp}_k(x_1\,y_1\,\ldots\,x_k\,y_k)\,$ demanding that the disjoint paths are within distance bigger than some fixed value $s$. Using the same technique we prove that model-checking for FOL+SDP can be done in quadratic time on classes of graphs with bounded Euler genus.\nJoint work with Petr A. Golovach and Dimitrios M. Thilikos.
URL:https://dimag.ibs.re.kr/event/2022-12-06/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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