Automating cutting planes is NP-hard

@article{Gs2020AutomatingCP,
  title={Automating cutting planes is NP-hard},
  author={Mika G{\"o}{\"o}s and Sajin Koroth and Ian Mertz and T. Pitassi},
  journal={Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing},
  year={2020}
}
We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula F, It is -hard to find a CP refutation of F in time polynomial in the length of the shortest such refutation; and unless Gap-Hitting-Set admits a nontrivial algorithm, one cannot find a tree-like CP refutation of F in time polynomial in the length of the shortest such refutation. The first result extends the recent breakthrough of Atserias and M'uller (FOCS 2019) that established an analogous result for… Expand
7 Citations
Automating Algebraic Proof Systems is NP-Hard
  • 5
On the Power and Limitations of Branch and Cut
  • 2
  • PDF
Automating Resolution is NP-Hard
  • PDF
Lifting with Sunflowers
Lifting: As Easy As 1, 2, 3
Chapter 7. Proof Complexity and SAT Solving
  • PDF
Log-rank and lifting for AND-functions
  • 1
  • PDF

References

Resolution Is Not Automatizable Unless W[P] Is Tractable
  • 96
  • Highly Influential
  • PDF