Revision #2 Authors: Noah Fleming, Denis Pankratov, Toniann Pitassi, Robert Robere

Accepted on: 9th September 2018 20:33

Downloads: 376

Keywords:

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.

- Re-wrote introduction.

- Numerical changes in proof of main theorem.

- Large editorial changes and notational simplification throughout.

Revision #1 Authors: Noah Fleming, Denis Pankratov, Toniann Pitassi, Robert Robere

Accepted on: 20th March 2017 20:22

Downloads: 956

Keywords:

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.

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

TR17-045 Authors: Noah Fleming, Denis Pankratov, Toniann Pitassi, Robert Robere

Publication: 7th March 2017 11:38

Downloads: 624

Keywords:

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.