Kernelizing MSO Properties of Trees of Fixed Height, and Some Consequences

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F15%3A00081185" target="_blank" >RIV/00216224:14330/15:00081185 - isvavai.cz</a>

Výsledek na webu

<a href="http://arxiv.org/pdf/1204.5194" target="_blank" >http://arxiv.org/pdf/1204.5194</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2168/LMCS-11(1:19)2015" target="_blank" >10.2168/LMCS-11(1:19)2015</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Kernelizing MSO Properties of Trees of Fixed Height, and Some Consequences

Popis výsledku v původním jazyce

We prove, in the universe of trees of bounded height, that for any MSO formula with $m$ variables there exists a set of kernels such that the size of each of these kernels can be bounded by an elementary function of $m$. This yields a faster MSO model checking algorithm for trees od bounded height than the one for general trees. From that we obtain, by means of interpretation, corresponding results for the classes of graphs of bounded tree-depth (MSO2) and shrub-depth (MSO1), and thus we give wide generalizations of Lampis' (ESA 2010) and Ganian's (IPEC 2011) results. In the second part of the paper we use this kernel structure to show that FO has the same expressive power as MSO1 on the graph classes of bounded shrub-depth. This makes bounded shrub-depth a good candidate for characterization of the hereditary classes of graphs on which FO and MSO1 coincide, a problem recently posed by Elberfeld, Grohe, and Tantau (LICS 2012).

Název v anglickém jazyce

Kernelizing MSO Properties of Trees of Fixed Height, and Some Consequences

Popis výsledku anglicky

We prove, in the universe of trees of bounded height, that for any MSO formula with $m$ variables there exists a set of kernels such that the size of each of these kernels can be bounded by an elementary function of $m$. This yields a faster MSO model checking algorithm for trees od bounded height than the one for general trees. From that we obtain, by means of interpretation, corresponding results for the classes of graphs of bounded tree-depth (MSO2) and shrub-depth (MSO1), and thus we give wide generalizations of Lampis' (ESA 2010) and Ganian's (IPEC 2011) results. In the second part of the paper we use this kernel structure to show that FO has the same expressive power as MSO1 on the graph classes of bounded shrub-depth. This makes bounded shrub-depth a good candidate for characterization of the hereditary classes of graphs on which FO and MSO1 coincide, a problem recently posed by Elberfeld, Grohe, and Tantau (LICS 2012).

Druh

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

CEP obor

BA - Obecná matematika

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

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

26

Strana od-do

1-26

Kód UT WoS článku

000353193000002

EID výsledku v databázi Scopus

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