On matroid properties definable in the MSO logic

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Abstract

It has been proved by the author that all matroid properties definable in the monadic second-order (MSO) logic can be recognized in polynomial time for matroids of bounded branch-width which are represented by matrices over finite fields. (This result extends so called "MS2-theorem" of graphs by Courcelle and others.) In this work we review the MSO theory of finite matroids and show some interesting matroid properties which are MSO-definable. In particular, all minor-closed properties are recognizable in such way. © Springer-Verlag Berlin Heidelberg 2003.

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Hliněný, P. (2003). On matroid properties definable in the MSO logic. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2747, 470–479. https://doi.org/10.1007/978-3-540-45138-9_41

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