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The Computational Power of Bounded Arithmetic from the Predicative Viewpoint

  • Samuel R. Buss

This paper considers theories of bounded arithmetic that are predicative in the sense of Nelson, that is, theories that are interpretable in Robinson’s Q.We give a nearly exact characterization of functions that can be total in predicative bounded theories. As an upper bound, any such function has a polynomial growth rate and its bit-graph is in nondeterministic exponential time and in co-nondeterministic exponential time. In fact, any function uniquely defined in a bounded theory of arithmetic lies in this class. Conversely, any function that is in this class (provably in IΔ0+exp) can be uniquely defined and total in a (predicative) bounded theory of arithmetic.

Keywords

Function Symbol Bounded Theory Exponential Time Exact Characterization Polynomial Time Computable Function 
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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Samuel R. Buss
    • 1
  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA

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