On Characterizations of the Basic Feasible Functionals, Part II

On characterizations of the basic feasible functionals (Part I)

We introduce a typed programming formalism, type-2 inflationary tiered loop programs or ITLP2, that characterizes the type-2 basic feasible functionals. ITLP2 is based on Bellantoni and Cook’s [BC92] and Leivant’s [Lei95] type-theoretic characterization of polynomial-time and turns out to be closely related to Kapron and Cook’s [KC91, KC96] machine-based characterization of the type-2 basic fea...

Characterizations of the Basic Feasible Functionals of Finite Type (Extended Abstract)

Equivalence of K-functionals and modulus of smoothness for fourier transform

In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

Separating Notions of Higher-Type Polynomial-Time

In his paper on machine characterizations of feasible functionals at all simple types, Seth [Set95] introduced the higher-type complexity class D and conjectured that this class is strictly larger than BFF, the basic feasible functionals of Cook and Urquhart [CU93]. In this paper we clarify the nature of D by characterizing D−, a subclass of D, through a typed programming formalism and show D− ...

A proof-theoretic characterization of the basic feasible functionals

We provide a natural characterization of the type two Mehlhorn-CookUrquhart basic feasible functionals as the provably total type two functionals of our (classical) applicative theory PT introduced in [30], thus providing a proof of a result claimed in the conclusion of [30]. This further characterization of the basic feasible functionals underpins their importance as a key candidate for the no...