Completeness of an Axiomatization of Graph Isomorphism via Graph Rewriting in Coq
The labeled multigraphs of treewidth at most two can be described using a simple term language over which isomorphism 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.
Tue 21 Jan Times are displayed in time zone: Saskatchewan, Central America change
15:35 - 16:40: Formalized mathematics 1CPP at Maurepas Chair(s): Robert Y. LewisVrije Universiteit Amsterdam | |||
15:35 - 15:56 Talk | Formalising perfectoid spaces CPP Patrick MassotUniversité Paris Sud, Kevin BuzzardImperial College London, Johan CommelinUniversität Freiburg DOI Pre-print Media Attached File Attached | ||
15:56 - 16:18 Talk | A Constructive Formalization of the Weak Perfect Graph Theorem CPP Abhishek Kr SinghTata Institute of Fundamental Research Mumbai, Raja NatarajanTata Institute of Fundamental Research Mumbai DOI Pre-print Media Attached File Attached | ||
16:18 - 16:40 Talk | Completeness of an Axiomatization of Graph Isomorphism via Graph Rewriting in Coq CPP DOI Pre-print Media Attached |