Monadic second-order model-checking on decomposable matroids

Yann Strozecki
2011 Discrete Applied Mathematics  
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 one to build matroids of bounded branch-width. Finally, we
more » ... uce 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.
doi:10.1016/j.dam.2011.02.005 fatcat:33f6zing5zg4jnuqy4arvae47a