On decidability of MSO theories of combinatorial structures: Towards general matroids?
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F06%3A00024640" target="_blank" >RIV/00216224:14330/06:00024640 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
On decidability of MSO theories of combinatorial structures: Towards general matroids?
Original language 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 resemblesordinary 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 fieldimplies 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 "abstract", 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 "good" width measure for general
Czech name
O rozhodnutelnosti MSO teorií kombinatorických struktur: Obecné matroidy?
Czech description
Studujeme problém rozhodnutelnosti MSO teorií v kombinatorice se speciálním zřetelem na matroidy.
Classification
Type
O - Miscellaneous
CEP classification
IN - Informatics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA201%2F05%2F0050" target="_blank" >GA201/05/0050: Structural properties and algorithmic complexity of discrete problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2006
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů