Tomer Kotek ; Johann A. Makowsky - Connection Matrices and the Definability of Graph Parameters

lmcs:731 - Logical Methods in Computer Science, October 31, 2014, Volume 10, Issue 4 - https://doi.org/10.2168/LMCS-10(4:1)2014
Connection Matrices and the Definability of Graph Parameters

Authors: Tomer Kotek ; Johann A. Makowsky

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.


Volume: Volume 10, Issue 4
Published on: October 31, 2014
Submitted on: August 16, 2013
Keywords: Computer Science - Logic in Computer Science,Mathematics - Combinatorics


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