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• W4313227384 abstract "It is well-known that Resolution proofs can be efficiently simulated by Sherali-Adams (SA) proofs. We show <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sup> , 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 $nsubseteq$ PPP, SOPL $nsubseteq$ PPA, and EOPL $nsubseteq$ 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. <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sup> This is an extended abstract. For the full version of this article, please refer to [GHJ+22b]." @default.
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• W4313227384 date "2022-10-01" @default.
• W4313227384 modified "2023-09-25" @default.
• W4313227384 title "Separations in Proof Complexity and TFNP" @default.
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• W4313227384 doi "https://doi.org/10.1109/focs54457.2022.00111" @default.
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