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Connection Matrices and the Definability of Graph Parameters

Authors Tomer Kotek, Johann A. Makowsky



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LIPIcs.CSL.2012.411.pdf
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Tomer Kotek
Johann A. Makowsky

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Tomer Kotek and Johann A. Makowsky. Connection Matrices and the Definability of Graph Parameters. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 411-425, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)
https://doi.org/10.4230/LIPIcs.CSL.2012.411

Abstract

In this paper we extend the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with modular counting CMSOL of B. Godlin, T. Kotek and J.A. Makowsky (2008 and 2009), and 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.
Keywords
  • Model theory
  • finite model theory
  • graph invariants

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