On characterizations of the basic feasible functionals (Part I)

On Characterizations of the Basic Feasible Functionals, Part II

Dept. of Elec. Eng. and Computer Science; Syracuse University; Syracuse, NY 13244 USA. Email: [email protected]. Research supported in part by NSF grant CCR-9522987. Dept. of Computer Science; University of Victoria; Victoria, BC V8W 3P6 Canada. Email: [email protected]. Dept. of Elec. Eng. and Computer Science; Syracuse University; Syracuse, NY 13244 USA. Email: [email protected]....

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

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...

Characterizing polynomial time complexity of stream programs using interpretations

This paper provides a criterion based on interpretation methods on term rewrite systems in order to characterize the polynomial time complexity of second order functionals. For that purpose it introduces a first order functional stream language that allows the programmer to implement second order functionals. This characterization is extended through the use of exp-poly interpretations as an at...