J. Kraj'icek. On the weak pigeonhole principle. Fund. Math. 170(1-3) pp. 123--140, 2001. Home/Search Document Not in Database Summary Related Articles Check |
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A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
....refutations. 1 Introduction This is an extended abstract. For a full version of the paper, please visit the web page http: www.cs. ucsd.edu nsegerli This paper studies the complexity of Res(k) a propositional refutation system that extends resolution by allowing k DNFs instead of clauses [24]. The complexity of propositional proof systems has close connections to # Supported in part by NSF grant DMS 0100589 and CCR0098197. Supported in part by NSF grant DMS 0100589. # Supported in part by NSF grant CCR 0098197 and USA Israel BSF Grant 97 00188. open problems in computational and ....
....provide a transition between resolution and depth two Frege. Moreover, statements provable in the theory T 2 (#) a fragment of Peano s arithmetic that allows induction only on # b 2 predicates) correspond to propositional statements with quasi polynomial size Res(polylog(n) refutations [24]. T 2 is the weakest fragment of Peano s arithmetic known to be able to use counting arguments such as the weak pigeonhole principle [25] On the other hand, these counting tautologies are known to be hard for resolution. Thus, there must be a critical range for k between 1 and polylog(n) where ....
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J. Krajcek. On the weak pigeonhole principle. Fudamenta Mathematicae, 170:123--140, 2001.
Pseudorandom Generators Hard for k-DNF Resolution and Polynomial .. - Razborov (2003) (7 citations) (Correct)
....This omnipresent hardness assumption is nothing else as the existence of pseudorandom generators (arbitrary or specific) which also turns out to be the main primitive of the modern cryptography. After the (apparent) failure of the e#cient interpolation approach, it was independently proposed in [Kra01a, ABRW00] to employ pseudorandom generators for proving conditional lower bounds in a more direct manner. On the conceptual level, a mapping G n : where m n, is called hard for a propositional proof system P if P can not e#ciently prove the (properly encoded) statement G n (x 1 , ....
....theory) that is opposite to the ordinary O notation. For example, given two functions f, g with values in the set of non negative reals, f ## g) means that there exists an absolute constant # 0 such that f #g for any specification of the parameters occurring in f, g. Definition 2. 1 ( Kra01a, ABRW00] Let m n, C be a Boolean circuit with n inputs x 1 , x n and m outputs, and b be an arbitrary Boolean vector. For every computational gate v of the circuit C we introduce a special extension variable y v , and when v is the jth input gate, we identify y v with the ....
J. Krajcek. On the weak pigeonhole principle. Fundamenta Mathematicae, 170(1-3):123--140, 2001.
On the Complexity of Resolution with Bounded Conjunctions - Esteban, Galesi, Messner (2004) (5 citations) (Correct)
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J. Kraj'icek. On the weak pigeonhole principle. Fund. Math. 170(1-3) pp. 123--140, 2001.
Feasible Proofs and Computations: Partnership and Fusion - Alexander Razborov Institute (Correct)
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J. Krajcek. On the weak pigeonhole principle. Fundamenta Mathematicae, 170(1-3):123--140, 2001.
A Switching Lemma for Small Restrictions and Lower.. - Segerlind, Buss.. (2002) (5 citations) (Correct)
No context found.
J. Krajcek. On the weak pigeonhole principle. Fudamenta Mathematicae, 170:123--140, 2001.
On the Automatizability of Resolution and Related.. - Atserias, Bonet (2003) (8 citations) (Correct)
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J. Krajcek. On the weak pigeonhole principle. Fundamenta Mathematic, 170(1-- 3):123--140, 2001.
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