TY - JOUR
T1 - Near optimal separation of tree-like and general resolution
AU - Ben-Sasson, Eli
AU - Impagliazzo, Russell
AU - Wigderson, Avi
PY - 2004
Y1 - 2004
N2 - 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)).
AB - 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)).
UR - http://www.scopus.com/inward/record.url?scp=16244414631&partnerID=8YFLogxK
U2 - 10.1007/s00493-004-0036-5
DO - 10.1007/s00493-004-0036-5
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:16244414631
SN - 0209-9683
VL - 24
SP - 585
EP - 603
JO - Combinatorica
JF - Combinatorica
IS - 4
ER -