Abstract

Using a function algebra characterization of exponential time due to Monien [5], in the style of Bellantoni-Cook [2], we characterize exponential time functions of linear growth via a safe course-of-values recursion scheme. 1 Introduction In 1991 [2], S. Bellantoni and S.A. Cook characterized the class FP of polynomial time computable functions as the smallest class of functions containing certain initial functions, and closed under safe composition and safe recursion on notation. In 1965, A. Cobham had earlier characterized FP in a similar manner using composition and bounded recursion on notation, where f is defined by bounded recursion on notation from g, h 0 , h 1 , k, if f(0; ~y) = g(~y) f(2x; ~y) = h 0 (x; ~y; f(x; ~y)); if x 6= 0 f(2x + 1; ~y) = h 1 (x; ~y; f(x; ~y)); provided that f(x; ~y) k(x; ~y). In addition to removing an initial function required by Cobham for polynomial growth rate, the novelty of the Bellantoni-Cook construction was to remove the bounding requiremen...

Citations

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