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

Christian Doczkal; Damien Pous

doi:10.1145/3372885.3373831

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

Christian Doczkal ^{1, 2, 3, 4, 5} Damien Pous ^{3, 1}

1 LIP - Laboratoire de l'Informatique du Parallélisme

2 MARELLE - Mathematical, Reasoning and Software

CRISAM - Inria Sophia Antipolis - Méditerranée

3 PLUME - Preuves et Langages

LIP - Laboratoire de l'Informatique du Parallélisme

4 STAMP - Sûreté du logiciel et Preuves Mathématiques Formalisées

CRISAM - Inria Sophia Antipolis - Méditerranée

5 UCA - Université Côte d'Azur

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.

Keywords : Rewriting Treewidth Algebra Graphs Coq

Document type :

Conference papers

Domain :

Computer Science [cs] / Logic in Computer Science [cs.LO]

Complete list of metadatas

Cited literature [18 references] Display Hide Download

https://hal.archives-ouvertes.fr/hal-02333553
Contributor : Christian Doczkal <>
Submitted on : Wednesday, January 8, 2020 - 6:08:43 PM
Last modification on : Wednesday, January 22, 2020 - 4:35:20 PM

coq-2pdom (1).pdf

Files produced by the author(s)

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

File

Identifiers

Collections

Citation

Export

Metrics

46

22

Contact

Informations

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

File

Identifiers

Collections

Citation

Export

Share

Metrics

46

22

Contact

Informations