by Maria Luisa Bonet, Toniann Pitassi, Ran Raz
http://www.wisdom.weizmann.ac.il/~ranraz/./publications/Ptonimari.ps
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Abstract:
The interpolation method has been one of the main tools for proving lower bounds for propositional proof systems. Loosely speaking, if one can prove that a particular proof system has the feasible interpolation property, then a generic reduction can (usually) be applied to prove lower bounds for the proof system, sometimes assuming a (usually modest) complexity-theoretic assumption. In this paper, we show that this method cannot be used to obtain lower bounds for Frege systems, or even for TC 0-Frege systems. More specifically, we show that unless factoring (of Blum integers) is feasible, neither Frege nor TC 0-Frege has the feasible interpolation property. In order to carry out our argument, we show how to carry out proofs of many elementary axioms/theorems of arithmetic in polynomial size TC 0
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