Exponential time and bounded arithmetic

Extended abstract
  • Peter Clote
  • Gaisi Takeuti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 223)


For each n, we give weak theories of bounded arithmetic, whose provably recursive functions (having appropriate graphs) are exactly those functions computable deterministically in n-fold time TIME(2(n,p(|x|))), where p is a polynomial and 2(n,z) is a stack of n two's topped by a z. In proving this result, we separate out the time contribution due to different variables in a multivariate function. These results further the evidence that “normalized” formal logic proofs (free cut free proof in Gentzen sequent calculus) of the totality of a function furnish an algorithm to compute the function.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Peter Clote
    • 1
  • Gaisi Takeuti
    • 2
  1. 1.Department of Computer ScienceBoston CollegeUSA
  2. 2.Department of MathematicsUniversity of Illinois at UrbanaUSA

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