From Proofs to Computations
- 14:00 27th June 2019 ( week 9, Trinity Term 2019 )Lecture Theatre B, Wolfson Building
For any unsatisfiable CNF formula F that is hard to refute in the Resolution proof system, we show that a gadget-composed version of F is hard to refute in any proof system whose lines are computed by efficient communication protocols --- or, equivalently, that a monotone function associated with F has large monotone circuit complexity. Our result extends to monotone real circuits, which yields new lower bounds for the Cutting Planes proof system. As an application, we show that a monotone version of the XOR-SAT function has exponential monotone circuit complexity. Since XOR-SAT is in NC^2, this improves qualitatively on the monotone vs. non-monotone separation of Tardos (1988). Another corollary is that monotone span programs can be exponentially more powerful than monotone circuits.