Near optimal separation of tree-like and general resolution

Eli Ben-Sasson*, Russell Impagliazzo, Avi Wigderson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

81 Scopus citations

Abstract

We present the best known separation between tree-like and general resolution, improving on the recent exp(nε) separation of [2]. This is done by constructing a natural family of contradictions, of size n, that have O(n)-size resolution refutations, but only exp(Ω(n/log n))-size tree-like refutations. This result implies that the most commonly used automated theorem procedures, which produce tree-like resolution refutations, will perform badly on some inputs, while other simple procedures, that produce general resolution refutations, will have polynomial run-time on these very same inputs. We show, furthermore that the gap we present is nearly optimal. Specifically, if S (ST) is the minimal size of a (tree-like) refutation, we prove that ST = exp(O(S log log S/log S)).

Original languageEnglish
Pages (from-to)585-603
Number of pages19
JournalCombinatorica
Volume24
Issue number4
DOIs
StatePublished - 2004

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