S. Buss. Propositional consistency proofs. Annals of Pure and Applied Logic, 52:3--29, 1991. Home/Search Document Details and Download
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Relating the Provable Collapse of P to NC¹ and the Power of.. - Cook (Correct)
.... 1;b 0 theorem of the second order theory U 1 1 corresponds to a sequence of tautologies with quasi polynomial size Frege proofs, but apparently no one has yet defined a satisfactory second order theory that nicely corresponds to polynomial size Frege proofs (see [Kra95b] page 297) Buss [Bus91] proved that Frege systems have polynomial size partial selfconsistency proofs. Arai showed how to formalize this in his system AID, to show that AID proves the soundness of Frege proof systems. Buss also showed that Frege systems have polynomial size proofs of partial consistency of extended ....
....are equivalent: 1. QPV is 8 Pi b 1 conservative over AID. 2. AID proves the soundness of extended Frege systems. 3. AID proves that Frege systems p simulate extended Frege systems. Proof sketch: 1 = 2: QPV proves the soundness of extended Frege systems [Coo75] and using the methods of [Bus91] and [Ara91] this soundness assertion can be formulated as a 8 Pi b 1 sentence in AID. 2 = 3: Formalize Buss s theorem [Bus91] in AID. 3 = 1: Let A be a 8 Pi b 1 formula of AID which is provable in QPV. Then by results in [Coo75] see [Kra95a] A gives rise to a sequence of ....
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S. R. Buss, Propositional consistency proofs, Annals of Pure and Applied Logic 52 (1991), 3--29.
Cutting plane and Frege proofs - Clote (Correct)
....Key Lemma leads to the simulation of Frege systems (without the restriction to constant depth) by CPLE and for making a number of other comments. The direct analysis suggested by S.R. Buss is carried out in this paper; S.R. Buss also noted an alternate proof of the Key Lemma, using results of [7] together with the weaker form of the Key Lemma appearing in [10] Namely, it follows from [7] that if OE has a Frege proof of size s, then there is a Frege proof of size s O(1) and depth O(log s) hence a tree like Frege proof of size s O(1) and depth O(log s) This, together with the weaker ....
....by CPLE and for making a number of other comments. The direct analysis suggested by S.R. Buss is carried out in this paper; S.R. Buss also noted an alternate proof of the Key Lemma, using results of [7] together with the weaker form of the Key Lemma appearing in [10] Namely, it follows from [7] that if OE has a Frege proof of size s, then there is a Frege proof of size s O(1) and depth O(log s) hence a tree like Frege proof of size s O(1) and depth O(log s) This, together with the weaker version of the Key Lemma of [10] suffices to obtain the polynomial simulation of Frege systems ....
S.R. Buss. Propositional consistency proofs. Annals of Pure and Applied Logic, 52:3--29, 1991.
Quantified Propositional Calculus and a Second-Order Theory.. - Cook, Morioka (2004) (1 citation) (Correct)
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S. Buss. Propositional consistency proofs. Annals of Pure and Applied Logic, 52:3--29, 1991.
A Complexity Gap for Tree-Resolution - Riis (1999) (7 citations) (Correct)
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Buss, S.: Propositional consistency proofs, Annals of Pure and Applied
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