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Completeness of an Axiomatization of Graph Isomorphism via Graph Rewriting in Coq

Abstract : The labeled multigraphs of treewidth at most two can be described using a simple term language over which isomor-phism of the denoted graphs can be finitely axiomatized. We formally verify soundness and completeness of such an axiomatization using Coq and the mathematical components library. The completeness proof is based on a normalizing and confluent rewrite system on term-labeled graphs. While for most of the development a dependently typed representation of graphs based on finite types of vertices and edges is most convenient, we switch to a graph representation employing a fixed type of vertices shared among all graphs for establishing confluence of the rewrite system. The completeness result is then obtained by transferring confluence from the fixed-type setting to the dependently typed setting.
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https://hal.archives-ouvertes.fr/hal-02333553
Contributor : Christian Doczkal <>
Submitted on : Wednesday, January 8, 2020 - 6:08:43 PM
Last modification on : Thursday, January 21, 2021 - 1:34:13 PM
Long-term archiving on: : Thursday, April 9, 2020 - 11:45:16 PM

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Christian Doczkal, Damien Pous. Completeness of an Axiomatization of Graph Isomorphism via Graph Rewriting in Coq. CPP 2020 - 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, Jan 2020, New Orleans, LA, United States. ⟨10.1145/3372885.3373831⟩. ⟨hal-02333553v3⟩

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