Automata Approach to Graphs of Bounded Rank-width

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F08%3A00027038" target="_blank" >RIV/00216224:14330/08:00027038 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Automata Approach to Graphs of Bounded Rank-width
Original language 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-widthwas 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.
Czech name
Automatové zpracování grafů omezené rank-width
Czech description
V příspěvku popisujeme nový nezávislý popis rankové dekompozice grafu pomocí speciálních parsovacích stromů. V tomto popisu následně ukazujeme ekvivalent Myhill-Nerodovy věty a jeho použití v návrhu algoritmů pro grafy omezené rank-width.

Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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