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