Recognisability Equals Definability for Finitely Representable Matroids of Bounded Path-Width
Let {\mathbb{F}} be a finite field. We prove that there is an MSO-transduction which, given an {\mathbb{F}}-representable matroid of path-width k, produces a branch-decomposition of width at most f(k), for some function f. As a corollary, any recognizable property of {\mathbb{F}}-representable matro...
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| Vydáno v: | 2025 40th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) s. 678 - 690 |
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23.06.2025
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| Abstract | Let {\mathbb{F}} be a finite field. We prove that there is an MSO-transduction which, given an {\mathbb{F}}-representable matroid of path-width k, produces a branch-decomposition of width at most f(k), for some function f. As a corollary, any recognizable property of {\mathbb{F}}-representable matroids with bounded path-width is definable in MSO logic, and therefore recognizability is equivalent to MSO-definability on classes of {\mathbb{F}}-representable matroids of bounded path-width. This generalizes the result of Bojańczyk, Grohe and Pilipczuk [Logical Methods in Computer Science 17(1), 2021] which asserts the equivalence of the two notions on graphs of bounded linear clique-width. |
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| AbstractList | Let {\mathbb{F}} be a finite field. We prove that there is an MSO-transduction which, given an {\mathbb{F}}-representable matroid of path-width k, produces a branch-decomposition of width at most f(k), for some function f. As a corollary, any recognizable property of {\mathbb{F}}-representable matroids with bounded path-width is definable in MSO logic, and therefore recognizability is equivalent to MSO-definability on classes of {\mathbb{F}}-representable matroids of bounded path-width. This generalizes the result of Bojańczyk, Grohe and Pilipczuk [Logical Methods in Computer Science 17(1), 2021] which asserts the equivalence of the two notions on graphs of bounded linear clique-width. |
| Author | Oum, Sang-il Guillon, Bruno Kim, Eun Jung Campbell, Rutger Kante, Mamadou Moustapha |
| Author_xml | – sequence: 1 givenname: Rutger surname: Campbell fullname: Campbell, Rutger email: rutger@ibs.re.kr organization: Institute for Basic Science,Discrete Mathematics Group,Daejeon,Korea – sequence: 2 givenname: Bruno surname: Guillon fullname: Guillon, Bruno email: bruno.guillon@uca.fr organization: Université Clermont Auvergne,Clermont Auvergne INP, LIMOS, CNRS,Clermont-Ferrand,France – sequence: 3 givenname: Mamadou Moustapha surname: Kante fullname: Kante, Mamadou Moustapha email: mamadou.kante@uca.fr organization: Université Clermont Auvergne,Clermont Auvergne INP, LIMOS, CNRS,Clermont-Ferrand,France – sequence: 4 givenname: Eun Jung surname: Kim fullname: Kim, Eun Jung email: eunjung.kim@kaist.ac.kr organization: Institute for Basic Science,School of Computing, KAIST and Discrete Mathematics Group,Daejeon,Korea – sequence: 5 givenname: Sang-il surname: Oum fullname: Oum, Sang-il email: sangil@ibs.re.kr organization: Institute for Basic Science,Discrete Mathematics Group,Daejeon,Korea |
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| Snippet | Let {\mathbb{F}} be a finite field. We prove that there is an MSO-transduction which, given an {\mathbb{F}}-representable matroid of path-width k, produces a... |
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| SubjectTerms | branch-width Computer science decomposition-width definability Galois fields Logic matroid monadic second-order logic path-width recognisability transduction |
| Title | Recognisability Equals Definability for Finitely Representable Matroids of Bounded Path-Width |
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