In order to apply canonical labelling of graphs and isomorphism checking in interactive theorem provers, these checking algorithms must either be mechanically verified or their results must be verifiable by independent checkers. We analyze a state-of-the-art algorithm for canonical labelling of graphs (described by McKay and Piperno) and formulate it in terms of a formal proof system. We provide an implementation that can export a proof that the obtained graph is the canonical form of a given graph. Such proofs are then verified by our independent checker and can be used to confirm that two given graphs are not isomorphic.
In order to be able to apply graph isomorphism checking within interactive theorem provers, either graph isomorphism checking algorithms must be mechanically verified, or their results must be verifiable by independent checkers. We analyze a stateof-the-art graph isomorphism checking algorithm (described by McKay and Piperno) and formulate it in a form of a formal proof system. We provide an implementation that can export a proof that an obtained graph is the canonical form of a given graph. Such proofs are then verified by our independent checker, and are used to certify that two given graphs are non-isomorphic.
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