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.
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