Monadic second-order model-checking on decomposable matroids

Details Monadic second-order model-checking on decomposable matroids Monadic second-order model-checking on decomposable matroids

2009-08-31

arxiv.org/abs/0908.4499v2

Computer Science

Discrete Mathematics

32 pages, journal paper. Revision: the last part has been removed and the writing improved

Scientific paper

A notion of branch-width, which generalizes the one known for graphs, can be defined for matroids. We first give a proof of the polynomial time model-checking of monadic second-order formulas on representable matroids of bounded branch-width, by reduction to monadic second-order formulas on trees. This proof is much simpler than the one previously known. We also provide a link between our logical approach and a grammar that allows to build matroids of bounded branch-width. Finally, we introduce a new class of non-necessarily representable matroids, described by a grammar and on which monadic second-order formulas can be checked in linear time.

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