J. Kraj cek, Lower bounds to the size of constant-depth propositional proofs. Journal of Symbolic Logic, 59(1) (1994) 73-86. Home/Search Document Details and Download
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On Chvátal Rank and Cutting Planes Proofs - Atserias, Bonet, Levy (Correct)
.... that cutting planes refutations could be balanced, that is, suppose that a cutting planes refutation of length m could be transformed to a cutting planes refutation of height O(log m) We note that this sort of structural result holds for proof systems such as Frege, or even bounded depth Frege [Kra94] Obviously, the height of a refutation is a bound on the Chv atal rank since it bounds the number of rounds of applications of the Chv atal Gomory cut. This would imply that if the set of clauses requires Chv atal rank d) then it requires length 2 d) to refute in cutting planes. ....
J. Krajcek. Lower bounds to the size of constant-depth propositional proofs. Journal of Symbolic Logic, 39(1):73-86, 1994.
The Cost of a Cycle is a Square - Carbone (1999) (1 citation) (Correct)
....and proofs. Several analogies between proofs and circuits have been observed and for a survey we refer the reader to [Pud96] One idea discussed there (pp.612 618) and which was used to prove lower bounds for propositional proof systems, concerns effective interpolation. It is due to Kraj icek [Kra94] and can be stated as follows: suppose we can show that the propositional implication A B does not have simple interpolant I (i.e. there is no formula I that is written with symbols used both in A and B and such that A I and I B are provable) then it cannot have a simple proof. Several ....
J. Kraj'icek. Lower bounds to the size of constant-depth propositional proofs. Journal of Symbolic Logic 59:73--86, 1994.
A Bottom-Up Approach to Foundations of Mathematics - Pudlak (Correct)
.... general we can take fragments of the quanti ed propositional calculus obtained by an appropriate restriction on the quanti er complexity of formulas [18] A large part of the activity is concentrated on proving lower bounds on the lengths of propositional proofs and we can report steady progress [1, 12, 13, 21, 31, 32]. Unfortunately the proof systems for which one can prove that they are not polynomially bounded are still much weaker than Extended Frege; even proving a superpolynomial lower bound for Frege systems would be a breakthrough. Thus we do not expect that concrete independent 1 sentences will be ....
J. Kraj cek, Lower bounds to the size of constant-depth propositional proofs, Journal of Symbolic Logic, 59, (1994) pp. 73-86.
On the Lengths of Proofs of Consistency - a Survey of Results - Pudlák (Correct)
....has been started by Cook [9] who was the first to realize the importance of the lower bounds on the lengths of proofs in propositional calculus and a relation of this problem to equational and first order theories. In this field there was quite a significant progress recently; to name just a few [10, 30, 1, 4, 2, 27]. After the famous result of Paris and Harrington [40] who proved independence of a concrete mathematical statement from Peano Arithmetic, we started to study fragments of arithmetic with an intention to prove eventually independence of some simpler (from the point of view of quantifier ....
Jan Kraj'icek. Lower bounds to the size of constant-depth propositional proofs. Journal of Symbolic Logic, 59(1):73--86, 1994.
The Complexity Of Propositional Proofs - Urquhart (1995) (65 citations) (Correct)
....Ajtai s proof is a highly ingenious blend of non standard models for number theory and combinatorics. Subsequent work by a number of authors simplified Ajtai s proof, first eliminating the use of non standard models [9] second improving the lower bound from super polynomial to exponential [39, 7, 49, 38]. Kraj cek [39] proved the first truly exponential lower bounds for bounded depth proofs, using modified versions of the pigeon hole formulas for each depth d . In the same paper, he also showed that depth d Frege systems cannot p simulate depth d 1 Frege systems. Shortly afterwards, Pitassi, ....
....highly ingenious blend of non standard models for number theory and combinatorics. Subsequent work by a number of authors simplified Ajtai s proof, first eliminating the use of non standard models [9] second improving the lower bound from super polynomial to exponential [39, 7, 49, 38] Kraj cek [39] proved the first truly exponential lower bounds for bounded depth proofs, using modified versions of the pigeon hole formulas for each depth d . In the same paper, he also showed that depth d Frege systems cannot p simulate depth d 1 Frege systems. Shortly afterwards, Pitassi, Beame and ....
Jan Kraj cek, Lower bounds to the size of constant-depth propositional proofs, Journal of Symbolic Logic, vol. 59 (1994), pp. 73--86.
A Note on Conservativity Relations among Bounded.. - Impagliazzo.. Self-citation (Kraj) (Correct)
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J. Kraj cek, Lower bounds to the size of constant-depth propositional proofs. Journal of Symbolic Logic, 59(1) (1994) 73-86.
Combinatorics of First Order Structures and Propositional Proof.. - Krajicek Self-citation (Kraj) (Correct)
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J. Kraj cek, Lower bounds to the size of constant-depth propositional proofs. Journal of Symbolic Logic, 59(1) (1994) 73-86.
Bounded Arithmetic and Constant Depth Frege Proofs - Buss (2004) (Correct)
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J. Kraj cek, Lower bounds to the size of constant-depth propositional proofs, Journal of Symbolic Logic, 59 (1994), pp. 73--85.
Polynomial-size Frege and Resolution Proofs of st-Connectivity and .. - Buss (2003) (2 citations) (Correct)
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J. Kraj cek, Lower bounds to the size of constant-depth propositional proofs, Journal of Symbolic Logic, 59 (1994), pp. 73--85.
Pseudorandom Generators Hard for k-DNF Resolution and Polynomial .. - Razborov (2003) (7 citations) (Correct)
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J. Krajcek. Lower bounds to the size of constant-depth propositional proofs. Journal of Symbolic Logic, 59(1):73-86, 1994.
Polynomial-size Frege and Resolution Proofs of st-Connectivity and .. - Buss (2003) (2 citations) (Correct)
No context found.
J. Kraj cek, Lower bounds to the size of constant-depth propositional proofs, Journal of Symbolic Logic, 59 (1994), pp. 73--85.
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