Faster Existential FO Model Checking on Posets

D 2014

Faster Existential FO Model Checking on Posets

GAJARSKÝ, Jakub, Petr HLINĚNÝ, Jan OBDRŽÁLEK and Sebastian ORDYNIAK

Basic information

Original name

Faster Existential FO Model Checking on Posets

Authors

GAJARSKÝ, Jakub (703 Slovakia, belonging to the institution), Petr HLINĚNÝ (203 Czech Republic, guarantor, belonging to the institution), Jan OBDRŽÁLEK (203 Czech Republic, belonging to the institution) and Sebastian ORDYNIAK (276 Germany, belonging to the institution)

Edition

Berlin, ISAAC 2014, LNCS 8889, p. 441-451, 11 pp. 2014

Publisher

Springer International Publishing

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

Impact factor

Impact factor: 0.402 in 2005

RIV identification code

RIV/00216224:14330/14:00074016

Organization unit

Faculty of Informatics

ISBN

978-3-319-13074-3

ISSN

DOI

http://dx.doi.org/10.1007/978-3-319-13075-0_35

UT WoS

000354865900035

Keywords in English

existential first-order logic; parameterized complexity; kernelization; poset embedding

Abstract

V originále

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). 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 (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.

Links

GA14-03501S, research and development project

Name: Parametrizované algoritmy a kernelizace v kontextu diskrétní matematiky a logiky

Investor: Czech Science Foundation

MUNI/A/0765/2013, interní kód MU

Name: Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity (Acronym: SKOMU)

Investor: Masaryk University, Category A

MUNI/A/0855/2013, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace III. (Acronym: FI MAV III.)

Investor: Masaryk University, Category A

Citovat

GAJARSKÝ, Jakub, Petr HLINĚNÝ, Jan OBDRŽÁLEK and Sebastian ORDYNIAK. Faster Existential FO Model Checking on Posets. In Hee-Kap Ahn, Chan-Su Shin. ISAAC 2014, LNCS 8889. Berlin: Springer International Publishing, 2014, p. 441-451. ISBN 978-3-319-13074-3. Available from: https://dx.doi.org/10.1007/978-3-319-13075-0_35.

@inproceedings{1204410,
   author = {Gajarský, Jakub and Hliněný, Petr and Obdržálek, Jan and Ordyniak, Sebastian},
   address = {Berlin},
   booktitle = {ISAAC 2014, LNCS 8889},
   doi = {http://dx.doi.org/10.1007/978-3-319-13075-0_35},
   editor = {Hee-Kap Ahn, Chan-Su Shin},
   keywords = {existential first-order logic; parameterized complexity; kernelization; poset embedding},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Berlin},
   isbn = {978-3-319-13074-3},
   pages = {441-451},
   publisher = {Springer International Publishing},
   title = {Faster Existential FO Model Checking on Posets},
   year = {2014}
}

TY  - JOUR
ID  - 1204410
AU  - Gajarský, Jakub - Hliněný, Petr - Obdržálek, Jan - Ordyniak, Sebastian
PY  - 2014
TI  - Faster Existential FO Model Checking on Posets
PB  - Springer International Publishing
CY  - Berlin
SN  - 9783319130743
KW  - existential first-order logic
KW  - parameterized complexity
KW  - kernelization
KW  - poset embedding
N2  - 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). 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 (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.
ER  -

GAJARSKÝ, Jakub, Petr HLINĚNÝ, Jan OBDRŽÁLEK and Sebastian ORDYNIAK. Faster Existential FO Model Checking on Posets. In Hee-Kap Ahn, Chan-Su Shin. \textit{ISAAC 2014, LNCS 8889}. Berlin: Springer International Publishing, 2014, p.~441-451. ISBN~978-3-319-13074-3. Available from: https://dx.doi.org/10.1007/978-3-319-13075-0\_{}35.

Detailed Information on Publication Record