Publication details
On decidability of MSO theories of combinatorial structures: Towards general matroids?
| Authors | |
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| Year of publication | 2006 |
| MU Faculty or unit | |
| Citation | |
| 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 "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 matroids ? |