Faster Existential FO Model Checking on Posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F14%3A00074016" target="_blank" >RIV/00216224:14330/14:00074016 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-13075-0_35" target="_blank" >http://dx.doi.org/10.1007/978-3-319-13075-0_35</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-13075-0_35" target="_blank" >10.1007/978-3-319-13075-0_35</a>

Result language
angličtina
Original language name
Faster Existential FO Model Checking on Posets
Original language description
We prove that the model checking problem for the existen- tial 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). Whilethere 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 (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) ? n 2 ) 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 comple- ment this result by showing that, under a certain complexity-theoretical assumption, the existential FO model checking problem does not have a polynomial kernel.
Czech name
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Czech description
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Project
<a href="/en/project/GA14-03501S" target="_blank" >GA14-03501S: Parameterized algorithms and kernelization in the context of discrete mathematics and logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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