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Proof Complexity

  • Pavel Pudlák
Chapter
  • 2.4k Downloads
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

The first section deals with classical results in proof theory and the lengths of proofs in first-order logic. We explain cut-elimination, Herbrand’s Theorem and ordinal analysis of first order theories. We present bounds on the increase of lengths of proofs in cut-elimination and some other speed-up results. The next two sections are about mainstream results in proof complexity. We explain how first-order theories are associated with complexity classes. Further, we show how these theories are associated with propositional proof systems. Feasible incompleteness, the topic treated in the last section, refers to results and conjectures that talk about the feasible versions of classical incompleteness theorems.

Keywords

Polynomial Time Boolean Function Turing Machine Proof System Search Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Pavel Pudlák
    • 1
  1. 1.ASCRPragueCzech Republic

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