Faster Existential FO Model Checking on Posets

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Authors

GAJARSKÝ Jakub HLINĚNÝ Petr OBDRŽÁLEK Jan ORDYNIAK Sebastian

Year of publication 2015
Type Article in Periodical
Magazine / Source Logical Methods in Computer Science
MU Faculty or unit

Faculty of Informatics

Citation
Web http://arxiv.org/pdf/1409.4433.pdf
Doi http://dx.doi.org/10.2168/LMCS-11(4:8)2015
Field Informatics
Keywords rst-order logic; partially ordered sets; model checking; parameterized complexity
Description We prove that the model checking problem for the existential fragment of first-order (FO) logic on partially ordered sets is fixed-parameter tractable (FPT) with respect to the formula and the width of a poset (the maximum size of an antichain). While there is a long line of research into FO model checking on graphs, the study of this problem on posets has been initiated just recently by Bova, Ganian and Szeider (CSL-LICS 2014), who proved that the existential fragment of FO has an FPT algorithm for a poset of fixed width. We improve upon their result in two ways: (1) the runtime of our algorithm is O(f(|\phi|,w)*n2) on n-element posets of width w, compared to O(g(|\phi|)*n^{h(w)}) of Bova et al., and (2) our proofs are simpler and easier to follow. We complement this result by showing that, under a certain complexity-theoretical assumption, the existential FO model checking problem does not have a polynomial kernel.
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