Faster Deciding 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%2F12%3A00057865" target="_blank" >RIV/00216224:14330/12:00057865 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2012.112" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2012.112</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2012.112" target="_blank" >10.4230/LIPIcs.FSTTCS.2012.112</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Faster Deciding 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

Faster Deciding 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

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP202%2F11%2F0196" target="_blank" >GAP202/11/0196: Třídy dobře strukturovaných kombinatorických objektů, šířkové parametry a návrh efektivních algoritmů</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

2012

Kód důvěrnosti údajů

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

Název statě ve sborníku

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2012)

ISBN

9783939897477

ISSN

1868-8969

e-ISSN

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Počet stran výsledku

12

Strana od-do

112-123

Název nakladatele

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, LIPICS

Místo vydání

Dagstuhl, Germany

Místo konání akce

India

Datum konání akce

1. 1. 2012

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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