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Lower bounds for prepositional proofs and independence results in bounded arithmetic

  • Alexander A. Razborov
Invited Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1099)

Abstract

We begin with a highly informal discussion of the role played by Bounded Arithmetic and propositional proof systems in the reasoning about the world of feasible computations. Then we survey some known lower bounds on the complexity of proofs in various propositional proof systems, paying special attention to recent attempts on reducing such bounds to some purely complexity results or assumptions. As one of the main motivations for this research we discuss provability of extremely important propositional formulae that express hardness of explicit Boolean functions with respect to various non-uniform computational models.

Keywords

Boolean Function Proof System Proof Theory Propositional Formula Interpolation Theorem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Alexander A. Razborov
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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