About: On decidability of MSO theories of combinatorial structures: Towards general matroids?

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We study the problem of decidability of MSO theories on various (restricted) matroid classes. When considering the matroids representable over a finite field (which is in structural sense similar to graphs embedded on a surface), the situation resembles ordinary graphs as incidence structures. The monadic second-order theory of all matroids over a finite field of bounded branch-width is decidable [H]. Conversely, the decidability of monadic second-order theory of a class of matroids over a finite field implies a bound on the branch-widths of the matroids in this class [HS]. The situation gets much more versatile and interesting when considering matroids in general (as %22abstract%22, without a particular representation). We shall focus mainly on this part, and present some particular observations and results, and mainly open questions and directions for future research. This is related to another interesting question already raised by [HS] : What could be a %22good%22 width measure for general matroids ? We study the problem of decidability of MSO theories on various (restricted) matroid classes. When considering the matroids representable over a finite field (which is in structural sense similar to graphs embedded on a surface), the situation resembles ordinary graphs as incidence structures. The monadic second-order theory of all matroids over a finite field of bounded branch-width is decidable [H]. Conversely, the decidability of monadic second-order theory of a class of matroids over a finite field implies a bound on the branch-widths of the matroids in this class [HS]. The situation gets much more versatile and interesting when considering matroids in general (as %22abstract%22, without a particular representation). We shall focus mainly on this part, and present some particular observations and results, and mainly open questions and directions for future research. This is related to another interesting question already raised by [HS] : What could be a %22good%22 width measure for general matroids ? (en)
Title	On decidability of MSO theories of combinatorial structures: Towards general matroids? On decidability of MSO theories of combinatorial structures: Towards general matroids? (en)
skos:prefLabel	On decidability of MSO theories of combinatorial structures: Towards general matroids? On decidability of MSO theories of combinatorial structures: Towards general matroids? (en)
skos:notation	RIV/00216224:14330/06:00024640!RIV10-GA0-14330___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GA201/05/0050)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Hliněný, Petr
http://linked.open.../riv/druhVysledku	O - Ostatní výsledky nezařaditelné do žádného z výše uvedených druhů výsledku
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	490297
http://linked.open...ai/riv/idVysledku	RIV/00216224:14330/06:00024640
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	MSO logic; matroid; MSO decidability; branch-width (en)
http://linked.open.../riv/klicoveSlovo	MSO decidability branch-width matroid MSO logic
http://linked.open...ontrolniKodProRIV	[83D24BEAE998]
http://linked.open...in/vavai/riv/obor	IN
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Structural properties and algorithmic complexity of discrete problems
http://linked.open...UplatneniVysledku	2006
http://linked.open...iv/tvurceVysledku	Hliněný, Petr
http://localhost/t...ganizacniJednotka	14330

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