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FO Model Checking on Posets of Bounded Width

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GAJARSKÝ Jakub HLINĚNÝ Petr OBDRŽÁLEK Jan ORDYNIAK Sebastian RAMANUJAN M.S. LOKSHTANOV Daniel SAURABH Saket

Druh Článek ve sborníku
Konference 56th Annual Symposium on Foundations of Computer Science, FOCS 2015
Fakulta / Pracoviště MU

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WWW sborník
Doi http://dx.doi.org/10.1109/FOCS.2015.63
Obor Informatika
Klíčová slova model checking; first-order logic; posets; width; metatheorem
Popis Over the past two decades the main focus of research into first-order (FO) model checking algorithms have been sparse relational structures-culminating in the FPT-algorithm by Grohe, Kreutzer and Siebertz for FO model checking of nowhere dense classes of graphs [STOC'14], with dense structures starting to attract attention only recently. Bova, Ganian and Szeider [LICS'14] initiated the study of the complexity of FO model checking on partially ordered sets (posets). Bova, Ganian and Szeider showed that model checking existential FO logic is fixed-parameter tractable (FPT) on posets of bounded width, where the width of a poset is the size of the largest antichain in the poset. The existence of an FPT algorithm for general FO model checking on posets of bounded width, however, remained open. We resolve this question in the positive by giving an algorithm that takes as its input an n-element poset P of width w and an FO logic formula and determines whether the formula holds on the poset in FPT quadratic time with respect to both the width of the poset and size of the formula.
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