The computational power of bounded arithmetic from the predicative viewpoint
نویسنده
چکیده
This paper considers theories of bounded arithmetic which are predicative in the sense of Nelson, that is, theories which are interpretable in Robinson’s Q . We give a nearly exact characterization of functions which can be total in predicative bounded theories. As an upper bound, any such function has 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 which is in this class (provably in I∆0 + exp) can be uniquely defined and total in a (predicative) bounded theory of arithmetic.
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