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Resolution Lower Bounds for the Weak Pigeonhole Principle
, 2001
"... We prove that any Resolution proof for the weak pigeon hole principle, with n holes and any number of pigeons, is of ), (for some global constant ffl ? 0). One corollary is that a certain propositional formulation of the statement NP 6ae P=poly does not have short Resolution proofs. ..."
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Cited by 46 (2 self)
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We prove that any Resolution proof for the weak pigeon hole principle, with n holes and any number of pigeons, is of ), (for some global constant ffl ? 0). One corollary is that a certain propositional formulation of the statement NP 6ae P=poly does not have short Resolution proofs.
Improved Resolution Lower Bounds for the Weak Pigeonhole Principle
 Electronic Colloquium on Computational Complexity
, 2001
"... Recently, Raz [Raz01] established exponential lower bounds on the size of resolution proofs of the weak pigeonhole principle. We give another proof of this result which leads to better numerical bounds. Specifically, we show that every resolution proof of PHP ..."
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Cited by 15 (2 self)
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Recently, Raz [Raz01] established exponential lower bounds on the size of resolution proofs of the weak pigeonhole principle. We give another proof of this result which leads to better numerical bounds. Specifically, we show that every resolution proof of PHP
P != NP , Propositional Proof Complexity, and Resolution Lower Bounds for the Weak Pigeonhole Principle
 IN PROCEEDINGS OF ICM’2002 (INTERNATIONAL CONGRESS OF MATHEMATICIANS), VOL. III
, 2002
"... Recent results established exponential lower bounds for the length of any Resolution proof for the weak pigeonhole principle. More formally, it was proved that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length ), (for a constant = 1 ..."
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Cited by 2 (0 self)
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Recent results established exponential lower bounds for the length of any Resolution proof for the weak pigeonhole principle. More formally, it was proved that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length ), (for a constant
Resolution and the weak pigeonhole principle
 IN CSL
, 1997
"... We give new upper bounds for resolution proofs of the weak pigeonhole principle. We also give lower bounds for treelike resolution proofs. We present a normal form for resolution proofs of pigeonhole principles based on a new monotone resolution rule. ..."
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Cited by 36 (3 self)
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We give new upper bounds for resolution proofs of the weak pigeonhole principle. We also give lower bounds for treelike resolution proofs. We present a normal form for resolution proofs of pigeonhole principles based on a new monotone resolution rule.
Exponential Lower Bounds for the Pigeonhole Principle
, 1992
"... In this paper we prove an exponential lower bound on the size of boundeddepth Frege proofs for the pigeonhole principle (PHP). We also obtain an ~(log log rz)depth lower bound for any polynomialsized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact ..."
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Cited by 121 (27 self)
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In this paper we prove an exponential lower bound on the size of boundeddepth Frege proofs for the pigeonhole principle (PHP). We also obtain an ~(log log rz)depth lower bound for any polynomialsized Frege proof of the pigeonhole principle. Our theorem nearly completes the search for the exact
On the Weak Pigeonhole Principle
, 2001
"... We investigate the proof complexity, in (extensions of) resolution and in bounded arithmetic, of the weak pigeonhole principle and of Ramsey theorem. In particular, we link the proof complexity of these two principles. Further we give lower bounds to the width of resolution proofs and to the size of ..."
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Cited by 76 (6 self)
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We investigate the proof complexity, in (extensions of) resolution and in bounded arithmetic, of the weak pigeonhole principle and of Ramsey theorem. In particular, we link the proof complexity of these two principles. Further we give lower bounds to the width of resolution proofs and to the size
Resolution Lower Bounds for the Weak Functional Pigeonhole Principle
 Theoretical Computer Science
, 2002
"... We show that every resolution proof of the functional version FPHP n of the pigeonhole principle (in which one pigeon may not split between several holes) must have size exp . This implies an exp bound when the number of pigeons m is arbitrary. ..."
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Cited by 17 (1 self)
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We show that every resolution proof of the functional version FPHP n of the pigeonhole principle (in which one pigeon may not split between several holes) must have size exp . This implies an exp bound when the number of pigeons m is arbitrary.
Lower Bounds for the Weak Pigeonhole Principle and Random Formulas beyond Resolution
, 2002
"... We work with an extension of Resolution, called Res(2), that allows clauses with conjunctions of two literals. In this system there are rules to introduce and eliminate such conjunctions. We prove that the weak pigeonhole principle PHP cn n and random unsatisfiable CNF formulas require exponentials ..."
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Cited by 33 (10 self)
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size proofs in this system. This is the strongest system beyond Resolution for which such lower bounds are known. As a consequence to the result about the weak pigeonhole principle, Res(log) is exponentially more powerful than Res(2). Also we prove that Resolution cannot polynomially simulate Res(2
Boosting a Weak Learning Algorithm By Majority
, 1995
"... We present an algorithm for improving the accuracy of algorithms for learning binary concepts. The improvement is achieved by combining a large number of hypotheses, each of which is generated by training the given learning algorithm on a different set of examples. Our algorithm is based on ideas pr ..."
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Cited by 516 (15 self)
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presented by Schapire in his paper "The strength of weak learnability", and represents an improvement over his results. The analysis of our algorithm provides general upper bounds on the resources required for learning in Valiant's polynomial PAC learning framework, which are the best general
The lexical nature of syntactic ambiguity resolution
 Psychological Review
, 1994
"... Ambiguity resolution is a central problem in language comprehension. Lexical and syntactic ambiguities are standardly assumed to involve different types of knowledge representations and be resolved by different mechanisms. An alternative account is provided in which both types of ambiguity derive fr ..."
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Cited by 556 (23 self)
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from aspects of lexical representation and are resolved by the same processing mechanisms. Reinterpreting syntactic ambiguity resolution as a form of lexical ambiguity resolution obviates the need for special parsing principles to account for syntactic interpretation preferences, reconciles a number
Results 1  10
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582,530