Branch-Width, Parse Trees, and Monadic Second-Order Logic for Matroids

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F06%3A00015569" target="_blank" >RIV/00216224:14330/06:00015569 - isvavai.cz</a>
Alternative codes found
RIV/61989100:27240/06:00013585
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Branch-Width, Parse Trees, and Monadic Second-Order Logic for Matroids
Original language description
We introduce ``matroid parse trees'' which, using only a limited amount of information at each node, can build up the vector representations of matroids of bounded branch-width over a finite field. We prove that if $mf M$ is a family of matroids described by a sentence in the monadic second-order logic of matroids, then there is a finite tree automaton accepting exactly those parse trees which build vector representations of the bounded-branch-width representable members of $mf M$. Since the cycle matroids of graphs are representable over any field, our result directly extends the so called ``$MS_2$-theorem'' for graphs of bounded tree-width by Courcelle, and others. Moreover, applications and relations in areas other than matroid theory can be found, like for rank-width of graphs, or in the coding theory.
Czech name
Branch-width, parsovací stromy a monadická logika druhého řádu pro matroidy
Czech description
Článek dokazuje obdobu tzv. MS2-věty pro matroidy reprezentované nad konečnými tělesy: Pro matroid reprezentovaný nad konečným tělesem s omezenou branch-width lze stromovými automaty rozhodnout všechny MSO definované vlastnosti.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F05%2F0050" target="_blank" >GA201/05/0050: Structural properties and algorithmic complexity of discrete problems</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2006
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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