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Erfan Khaniki
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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
Erfan Khaniki
  • 1.7k
  • 1
  • 11
  • 17