A proof-theoretic characterization of the basic feasible functionals

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...

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− ...

The Basic Theorem and its Consequences

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

Ergodic Theoretic Characterization of Left Amenable Lau Algebras

Parallel computable higher type functionals - Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on

The primary aim of this paper is to introduce higher type analogues of some familiar parallel complexity classes, and to show that these higher type classes can be characterized in significantly different ways. Recursion-theoretic, proof-theoretic and machine-theoretic characterizations are given for various classes, providing evidence of their naturalness. In this section, we motivate the appr...