Fall 2018

Monotone Circuit Lower Bounds from Resolution (Now with Applications!)

Tuesday, September 11th, 2018 4:00 pm4:30 pm

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Mika Göös (Harvard University)

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.