Higher type recursion, ramification and polynomial time

doi:10.1016/S0168-0072(00)00006-3

Annals of Pure and Applied Logic

Volume 104, Issues 1–3, 15 July 2000, Pages 17-30

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Abstract

It is shown how to restrict recursion on notation in all finite types so as to characterize the polynomial-time computable functions. The restrictions are obtained by using a ramified type structure, and by adding linear concepts to the lambda calculus.

MSC

03D15

03D20

68Q15

68Q42

68N15

03F03

03F10

03F35

Keywords

Higher type recursion

Lambda calculus

Normalisation

Ramified recursion

Polynomial time

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¹: The author was affiliated with LMU when this paper was written.