Monadic second-order model-checking on decomposable matroids

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. T...

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Vydáno v:Discrete Applied Mathematics Ročník 159; číslo 10; s. 1022 - 1039
Hlavní autor: Strozecki, Yann
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 28.06.2011
Témata:
Branch-width
Construction
Decomposition
Enumeration
Fixed-parameter complexity
Grammars
Graphs
Links
Mathematical models
Matroid representation
Monadic second-order logic
Proving
Series-parallel operation
Trees
Enumeration
Series-parallel operation
Matroid representation
Monadic second-order logic
Fixed-parameter complexity
Branch-width
ISSN:0166-218X, 1872-6771
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Shrnutí: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 introduce 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.
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ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2011.02.005