The complexity of propositional proofs

Bulletin of Symbolic Logic 13 (4):417-481 (2007)
Abstract
Propositional proof complexity is the study of the sizes of propositional proofs, and more generally, the resources necessary to certify propositional tautologies. Questions about proof sizes have connections with computational complexity, theories of arithmetic, and satisfiability algorithms. This is article includes a broad survey of the field, and a technical exposition of some recently developed techniques for proving lower bounds on proof sizes
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Samuel R. Buss (2012). Towards–Via Proof Complexity and Search. Annals of Pure and Applied Logic 163 (7):906-917.
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