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Theories for Complexity Classes and their Propositional Translations
 Complexity of computations and proofs
, 2004
"... We present in a uniform manner simple twosorted theories corresponding to each of eight complexity classes between AC and P. We present simple translations between these theories and systems of the quanti ed propositional calculus. ..."
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Cited by 33 (7 self)
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We present in a uniform manner simple twosorted theories corresponding to each of eight complexity classes between AC and P. We present simple translations between these theories and systems of the quanti ed propositional calculus.
Bounded arithmetic AID for Frege system
 Annals of Pure and Applied Logic
"... In this paper we introduce a system AID (Alogtime Inductive Denitions) of bounded arithmetic. The main feature of AID is to allow a form of inductive denitions, which was extracted from Buss ' propositional consistency proof of Frege systems F in [7]. We show that AID proves the soundness of ..."
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Cited by 13 (0 self)
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In this paper we introduce a system AID (Alogtime Inductive Denitions) of bounded arithmetic. The main feature of AID is to allow a form of inductive denitions, which was extracted from Buss ' propositional consistency proof of Frege systems F in [7]. We show that AID proves the soundness of F, and conversely any b 0theorem in AID yields boolean sentences of which F has polysize proofs. Further we dene
Several notes on the power of GomoryChvátal cuts
, 2003
"... We prove that the Cutting Plane proof system based on GomoryChvátal cuts polynomially simulates the liftandproject system with integer coecients written in unary. The restriction on coefficients can be omitted when using Krajícek's cutfree Gentzenstyle extension of both systems. We also ..."
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Cited by 3 (0 self)
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We prove that the Cutting Plane proof system based on GomoryChvátal cuts polynomially simulates the liftandproject system with integer coecients written in unary. The restriction on coefficients can be omitted when using Krajícek's cutfree Gentzenstyle extension of both systems. We also prove that Tseitin tautologies have short proofs in this extension (of any of these systems and with any coefficients).