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This is a Quantitative Study study (also classified as: Experimental Study).

September 20, 2025

Verified Certificates via SAT and Computer Algebra Systems for the Ramsey R(3,8) and R(3,9) Problems

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Authors

ZLZhengyu LiShanghai Jiao Tong University CDConor DugganUniversity of Waterloo CBCurtis BrightUniversity of Waterloo

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Implication

This research applies a SAT solver integrated with a computer algebra system to significantly improve certificate verification for Ramsey numbers R(3,8) and R(3,9).

Key Points

Our tailored SAT+CAS method demonstrated improved verification times, solving R(3,8) in 59 hours versus 7 days with traditional SAT methods.
The introduction of a parallelized cube-and-conquer approach further accelerated our method's capability to handle more complex Ramsey problems.
This work delivers the first independently verifiable certificates for R(3,8) and R(3,9), confirming the exhaustive search’s correctness and completeness.
We showed that integrating computer algebra systems with SAT solvers can yield significant improvements in computational complexity for Ramsey number problems.

Cite This Study

Li et al. (2025) studied this question.

synapsesocial.com/papers/68d46aa631b076d99fa672df https://doi.org/10.24963/ijcai.2025/292

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Implication

This research applies a SAT solver integrated with a computer algebra system to significantly improve certificate verification for Ramsey numbers R(3,8) and R(3,9).

Verified Certificates via SAT and Computer Algebra Systems for the Ramsey R(3,8) and R(3,9) Problems

Discussion

Member takes

Implication

Key Points

Cite This Study

Verified Certificates via SAT and Computer Algebra Systems for the Ramsey R(3,8) and R(3,9) Problems

Discussion

Member takes

Implication

Key Points

Cite This Study

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