## Near-Optimal Separation of Treelike and General Resolution (2000)

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Venue: | Electronic Colloquium in Computation Complexity |

Citations: | 47 - 3 self |

### BibTeX

@TECHREPORT{Ben-sasson00near-optimalseparation,

author = {Eli Ben-sasson and Russell Impagliazzo and Avi Wigderson},

title = {Near-Optimal Separation of Treelike and General Resolution},

institution = {Electronic Colloquium in Computation Complexity},

year = {2000}

}

### Years of Citing Articles

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### Abstract

We present the best known separation between tree-like and general resolution, improving on the recent exp(n ) separation of [BEGJ98].

### Citations

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Citation Context ... and investigated methods for proving unsatis ability of CNF formulas, are called Davis-Putnam procedures. Actually, these procedures are derived from a system devised by Davis, Logemann and Loveland =-=[DLL62-=-], and hence we will refer to them as DLL Procedures. A DLL procedure relies on choosing a variable x, and trying to refute T j x=T and T j x=F recursively. If T is unsatisable, DLL(T ) terminates pro... |

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- Ben-Sasson, Wigderson
(Show Context)
Citation Context ...ion systems (the previous best bound being the recent exp( p n) separation of [BEGJ98]). Finally, (3) means that for these contradictions, the natural \restricted-width" dynamic programming algor=-=ithm [BW99]-=-, that searches for a minimal width refutation, has polynomial time, which is exponentially faster than any recursive method. Theorem 1.2 uses techniques from [PV76], that showed that if a boolean fun... |

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Citation Context ...the graph G is an exponential lower bound on the tree-like size of refuting T (G). The connection of pebbling to tree-like size allows us to use graphs that have a high pebbling measure. Specically, [=-=CPT77]-=- explicitly construct for every n a graph G n of size O(n) satisfying P (G n ) =sn= log n). This, combined with (1) and the upper bound (2), gives a truly exponential separation between general and tr... |

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- 2000
(Show Context)
Citation Context ... one derives 0. 7 3.2 A game for proving lower bounds on tree-like resolution Lower bounds for size of tree-like resolution proofs can be given in terms of a 2-player game; this description is due to =-=[PI00]-=-. Any small tree-like proof will give a good strategy for one of the players, so a good strategy for the other player yields a corresponding lower bound on proofs. Let T be an inconsistent set of clau... |

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Circuit size is nonlinear in depth
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(Show Context)
Citation Context ...dth" dynamic programming algorithm [BW99], that searches for a minimal width refutation, has polynomial time, which is exponentially faster than any recursive method. Theorem 1.2 uses techniques =-=from [PV76], tha-=-t showed that if a boolean function has a circuit of size S then it has a circuit of depth S= log S. We use similar techniques to show that one can \cut" any general refutation roughly in half, b... |

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