On Decidability of MSO Theories of Representable Matroids
نویسندگان
چکیده
We show that, for every finite field , the class of all representable matroids of branch-width at most a constant t has a decidable MSO theory. In the other direction, we prove that every class of -representable matroids with a decidable MSO theory must have uniformly bounded branch-width.
منابع مشابه
Trees, grids, and MSO decidability: From graphs to matroids
Monadic second order (MSO) logic proved to be a useful tool in many areas of application, reaching from decidability and complexity to picture processing, correctness of programs and parallel processes. To characterize the structural borderline between decidability and undecidability is a classical research problem here. This problem is related to questions in computational complexity, especial...
متن کاملMonadic second-order model-checking on decomposable matroids
A notion of branch-width may be defined for matroids, which generalizes the one known for graphs. We first give a proof of the polynomial time model checking of MSOM on representable matroids of bounded branch-width, by reduction to MSO on trees, much simpler than the one previously known. We deduce results about spectrum of MSOM formulas and enumeration on matroids of bounded branch-width. We ...
متن کاملOn Representable Matroids Having Neither U2,5– Nor U3,5–minors
Consider 3–connected matroids that are neither binary nor ternary and have neither U2,5– nor U3,5–minors: for example, AG(3, 2)′, the matroid obtained by relaxing a circuit-hyperplane of AG(3, 2). The main result of the paper shows that no matroid of this sort is representable over any field. This result makes it possible to extend known characterisations of the binary and ternary matroids repr...
متن کاملOn Representable Matroids and Ideal Secret Sharing
In secret sharing, the exact characterization of ideal access structures is a longstanding open problem. Brickell and Davenport (J. of Cryptology, 1991) proved that ideal access structures are induced by matroids. Subsequently, ideal access structures and access structures induced by matroids have attracted a lot of attention. Due to the difficulty of finding general results, the characterizati...
متن کاملThe Excluded Minors for Gf(4)--representable Matroids the Excluded Minors for Gf(4){representable Matroids
There are exactly seven excluded minors for the class of GF(4){representable matroids. Note: The research for this paper was carried out under the PNA1.1-project P&BS of CWI, while J.F. Geelen and A. Kapoor visited the CWI in Amsterdam with nancial support from EIDMA.
متن کامل