English

Monadic second-order model-checking on decomposable matroids

Discrete Mathematics 2015-03-13 v2 Data Structures and Algorithms Logic in Computer Science

Abstract

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 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.

Keywords

Cite

@article{arxiv.0908.4499,
  title  = {Monadic second-order model-checking on decomposable matroids},
  author = {Yann Strozecki},
  journal= {arXiv preprint arXiv:0908.4499},
  year   = {2015}
}

Comments

32 pages, journal paper. Revision: the last part has been removed and the writing improved

R2 v1 2026-06-21T13:40:35.521Z