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I am asking if there are some good or standard references for proof complexity theory? I didn't find references when I search in internet. Thanks!

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These are three books that I know:

  1. Logical Foundations of Proof Complexity
  2. Bounded Arithmetic, Propositional Logic and Complexity Theory
  3. Logical Foundations of Mathematics and Computational Complexity, Proof complexity chapter

Also, I suggest you read the following papers:

  1. The lengths of proofs
  2. Bounded Arithmetic and Propositional Proof Complexity

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Update. Jan Krajíček wrote a new book on this topic recently. You can find the final manuscript of it here.

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