Verifying Faradžev-Read Type Isomorph-Free Exhaustive Generation

Marić, Filip

doi:10.1007/978-3-030-51054-1_16

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…The formal proof of Kepler's conjecture about the optimal packing of spheres in three-dimensional Euclidean space [HAB + 17] required the identification, enumeration and analysis of several thousand nonisomorphic graphs [Nip11], which was done using a custom formally verified algorithm. Initial steps to verify generic algorithms for the isomorph-free enumeration of combinatorial objects have been taken (e.g., the Faradžev-Read enumeration has been formally verified within Isabelle/HOL [Mar20]). Several other such algorithms (e.g., [McK98]) would benefit from trustworthy graph isomorphism checking, automorphism group computation, and canonical labelling.…”

Section: Introductionmentioning

confidence: 99%

A proof system for graph (non)-isomorphism verification

Banković¹,

Drecun²,

Marić³

2023

Logical Methods in Computer Science

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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.

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Section: Introductionmentioning

confidence: 99%

A proof system for graph (non)-isomorphism verification

Banković¹,

Drecun²,

Marić³

2023

Logical Methods in Computer Science

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“…There are many cases where such applications could benefit from checking graph isomorphism. For example, isomorphism checking can be used to enumerate and count isomorph-free families of some combinatorial objects [McK98,Nip11,Mar20]. In order to apply graph isomorphism checking in theorem proving applications, it needs to be verified.…”

Section: Introductionmentioning

confidence: 99%

A proof system for graph (non)-isomorphism verification

Banković¹,

Drecun²,

Marić³

2021

Preprint

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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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Verifying Faradžev-Read Type Isomorph-Free Exhaustive Generation

Cited by 2 publications

References 13 publications

A proof system for graph (non)-isomorphism verification

A proof system for graph (non)-isomorphism verification

A proof system for graph (non)-isomorphism verification

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