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Paper:

TR21-033 | 7th March 2021 22:39

Automating Tree-Like Resolution in Time $n^{o(\log n)}$ Is ETH-Hard

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TR21-033
Authors: Susanna de Rezende
Publication: 8th March 2021 07:13
Downloads: 144
Keywords: 


Abstract:

We show that tree-like resolution is not automatable in time $n^{o(\log n)}$ unless ETH is false. This implies that, under ETH, the algorithm given by Beame and Pitassi (FOCS 1996) that automates tree-like resolution in time $n^{O(\log n)}$ is optimal. We also provide a simpler proof of the result of Alekhnovich and Razborov (FOCS 2001) that unless the fixed parameter hierarchy collapses, tree-like resolution is not automatable in polynomial time. The proof of our results builds on a joint work with Göös, Nordström, Pitassi, Robere and Sokolov (STOC 2021), which presents a simplification of the recent breakthrough of Atserias and Müller (FOCS 2019).



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