Faster Existential FO Model Checking on Posets

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F15%3A00081186" target="_blank" >RIV/00216224:14330/15:00081186 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.2168/LMCS-11(4:8)2015" target="_blank" >http://dx.doi.org/10.2168/LMCS-11(4:8)2015</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2168/LMCS-11(4:8)2015" target="_blank" >10.2168/LMCS-11(4:8)2015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Faster Existential FO Model Checking on Posets

Popis výsledku v původním jazyce

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. Wecomplement this result by showing that, under a certain complexity-theoretical assumption, the existential FO model checking problem does not have a polynomial kernel.

Název v anglickém jazyce

Faster Existential FO Model Checking on Posets

Popis výsledku anglicky

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. Wecomplement this result by showing that, under a certain complexity-theoretical assumption, the existential FO model checking problem does not have a polynomial kernel.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GA14-03501S" target="_blank" >GA14-03501S: Parametrizované algoritmy a kernelizace v kontextu diskrétní matematiky a logiky</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Logical Methods in Computer Science

ISSN

1860-5974

e-ISSN

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Svazek periodika

11

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

13

Strana od-do

1-13

Kód UT WoS článku

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EID výsledku v databázi Scopus

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