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Diagonalization in proof complexity

Jan Krajíček (2004)

Fundamenta Mathematicae

We study diagonalization in the context of implicit proofs of [10]. We prove that at least one of the following three conjectures is true: ∙ There is a function f: 0,1* → 0,1 computable in that has circuit complexity 2 Ω ( n ) . ∙ ≠ co . ∙ There is no p-optimal propositional proof system. We note that a variant of the statement (either ≠ co or ∩ co contains a function 2 Ω ( n ) hard on average) seems to have a bearing on the existence of good proof complexity generators. In particular, we prove that if a minor variant...

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