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Branch-Width, Parse Trees, and Monadic Second-Order Logic for Matroids
[chapter]

2003
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Lecture Notes in Computer Science
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We introduce "matroid parse trees" which, using only a limited amount of information at each node, can build up the vector representations of matroids of bounded branch-width over a finite field. We prove that if M is a family of matroids described by a sentence in the monadic second-order logic of matroids, then there is a finite tree automaton accepting exactly those parse trees which build vector representations of the bounded-branch-width representable members of M. Since the cycle matroids

doi:10.1007/3-540-36494-3_29
fatcat:wsejm3qjovbjbbt6nfeetf4ypm