Connection Matrices and the Definability of Graph Parameters
Logic in Computer Science
2015-07-01 v4 Combinatorics
Abstract
In this paper we extend and prove in detail the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with counting (CMSOL) from B. Godlin, T. Kotek and J.A. Makowsky (2008) and J.A. Makowsky (2009). We demonstrate its vast applicability in simplifying known and new non-definability results of graph properties and finding new non-definability results for graph parameters. We also prove a Feferman-Vaught Theorem for the logic CFOL, First Order Logic with the modular counting quantifiers.
Cite
@article{arxiv.1308.3654,
title = {Connection Matrices and the Definability of Graph Parameters},
author = {Tomer Kotek and Johann A. Makowsky},
journal= {arXiv preprint arXiv:1308.3654},
year = {2015}
}