Tree Automata and Pigeonhole Classes of Matroids: II

Let $\psi$ be a sentence in the counting monadic second-order logic of matroids and let F finite field. Hlineny's Theorem says that we can test whether F-representable satisfy using an algorithm is fixed-parameter tractable with respect to branch-width. In previous paper proved there similar members any efficiently pigeonhole class. this sequel apply results from first thereby extend classes fundamental transversal matroids, lattice path bicircular H-gain-graphic when H group. As consequence, obtain new proof Courcelle's Theorem.