Date & Time:
October 18, 2022 3:30 pm – 4:30 pm
Location:
Kent 107, 1020-24 East 58th St., Chicago, IL, 60637
10/18/2022 03:30 PM 10/18/2022 04:30 PM America/Chicago Mika Göös (EPFL) – Separations in Proof Complexity and TFNP Kent 107, 1020-24 East 58th St., Chicago, IL, 60637

It is well-known that Resolution proofs can be efficiently simulated by Sherali-Adams (SA) proofs. We show, however, that any such simulation needs to exploit huge coefficients: Resolution cannot be efficiently simulated by SA when the coefficients are written in unary. We also show that Reversible Resolution (a variant of MaxSAT Resolution) cannot be efficiently simulated by Nullstellensatz (NS).

These results have consequences for total NP search problems. First, we characterise the classes PPADS, PPAD, SOPL by unary-SA, unary-NS, and Reversible Resolution, respectively. Second, we show that, relative to an oracle, PLS not-subset PPP, SOPL not-subset PPA, and EOPL not-subset UEOPL. In particular, together with prior work, this gives a complete picture of the black-box relationships between all classical TFNP classes introduced in the 1990s.

Host: Alexander Razborov

Speakers

Mika Göös

Assistant Professor, The Swiss Federal Institute of Technology in Lausanne, Switzerland

I am an assistant professor at EPFL in the Theory Group. Previously, I was a post-doc at Stanford, Princeton IAS, and Harvard.

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