2008 | OriginalPaper | Buchkapitel
The Computational Power of Bounded Arithmetic from the Predicative Viewpoint
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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.