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Revision #1 to TR17-045 | 20th March 2017 20:22

Random CNFs are Hard for Cutting Planes

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Revision #1
Authors: Noah Fleming, Denis Pankratov, Toniann Pitassi, Robert Robere
Accepted on: 20th March 2017 20:22
Downloads: 184
Keywords: 


Abstract:

The random k-SAT model is the most important and well-studied distribution over k-SAT instances. It is closely connected to statistical physics and is a benchmark for satisfiability algorithms. In this paper, we prove that any Cutting Planes refutation for random k-SAT requires exponential size, for k that is logarithmic in the number of variables, and in the interesting regime where the number of clauses guarantees that the formula is unsatisfiable with high probability.



Changes to previous version:

Minor edits throughout. Expanded Section 4.2, added Appendix and Conclusion.


Paper:

TR17-045 | 7th March 2017 05:49

Random CNFs are Hard for Cutting Planes





TR17-045
Authors: Noah Fleming, Denis Pankratov, Toniann Pitassi, Robert Robere
Publication: 7th March 2017 11:38
Downloads: 242
Keywords: 


Abstract:

The random k-SAT model is the most important and well-studied distribution over
k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for
satisfiablity algorithms, and lastly average-case hardness over this distribution has also
been linked to hardness of approximation via Feige’s hypothesis. In this paper, we prove
that any Cutting Planes refutation for random k-SAT requires exponential size, for k that
is logarithmic in the number of variables, and in the interesting regime where the number
of clauses guarantees that the formula is unsatisfiable with high probability.



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