About: Automata Approach to Graphs of Bounded Rank-width

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Rank-width is a rather new structural graph measure introduced by Oum and Seymour in 2003 in order to find an efficiently computable approximation of clique-width of a graph. Being a very nice graph measure indeed, the only serious drawback of rank-width was that it is virtually impossible to use a given rank-decomposition of a graph for running dynamic algorithms on it. We propose a new independent description of rank-decompositions of graphs using labeling parse trees which is, after all, mathematically equivalent to the recent algebraic graph-expression approach to rank-decompositions of Courcelle and Kant\'e [WG'07]. We then use our labeling parse trees to build a Myhill-Nerode-type formalism for handling restricted classes of graphs of bounded rank-width, and to directly prove that (an already indirectly known result) all graph properties expressible in MSO logic are decidable by finite automata running on the labeling parse trees. Rank-width is a rather new structural graph measure introduced by Oum and Seymour in 2003 in order to find an efficiently computable approximation of clique-width of a graph. Being a very nice graph measure indeed, the only serious drawback of rank-width was that it is virtually impossible to use a given rank-decomposition of a graph for running dynamic algorithms on it. We propose a new independent description of rank-decompositions of graphs using labeling parse trees which is, after all, mathematically equivalent to the recent algebraic graph-expression approach to rank-decompositions of Courcelle and Kant\'e [WG'07]. We then use our labeling parse trees to build a Myhill-Nerode-type formalism for handling restricted classes of graphs of bounded rank-width, and to directly prove that (an already indirectly known result) all graph properties expressible in MSO logic are decidable by finite automata running on the labeling parse trees. (en)
Title	Automata Approach to Graphs of Bounded Rank-width Automata Approach to Graphs of Bounded Rank-width (en)
skos:prefLabel	Automata Approach to Graphs of Bounded Rank-width Automata Approach to Graphs of Bounded Rank-width (en)
skos:notation	RIV/00216224:14330/08:00025022!RIV11-GA0-14330___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(1M0545), P(GA201/08/0308)
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Ganian, Robert Hliněný, Petr
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Fakulta informatiky
http://linked.open...dnocenehoVysledku	357363
http://linked.open...ai/riv/idVysledku	RIV/00216224:14330/08:00025022
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	parameterized algorithm; rank-width; tree automaton; MSO logic (en)
http://linked.open.../riv/klicoveSlovo	parameterized algorithm rank-width tree automaton MSO logic
http://linked.open...ontrolniKodProRIV	[B78C6012AA9C]
http://linked.open...v/mistoKonaniAkce	Nagoya, Japan
http://linked.open...i/riv/mistoVydani	United Kingdom
http://linked.open...i/riv/nazevZdroje	International Workshop on Combinatorial Algorithms IWOCA 2008
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Institute for Theoretical Computer Science Utilization of structural and %22Width%22 parameters in combinatorics and algorithmic complexity
http://linked.open...UplatneniVysledku	2008
http://linked.open...iv/tvurceVysledku	Ganian, Robert Hliněný, Petr
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2008-09-13 (xsd:date)
number of pages	12 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Proceedings of the International Workshop on Combinatorial Algorithms 2008, College Publications
https://schema.org/isbn	978-1-904987-74-1
http://localhost/t...ganizacniJednotka	14330

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