A well-known theorem of type-two recursion theory states that a functional is continuous if and only if it is computable relative to some oracle.

Abstract. A well-known theorem of type-two recursion theory states that a functional is continuous if and only if it is computable relative to some oracle.

Kapron [1999] presents a class of functionals which are feasibly continuous. Such functionals have certificates whose size is feasible, or polynomial, in terms ...

We define notions of resource-bounded continuity and sequentiality for type-two functionals with total inputs, and prove that in the resource-bounded model ...

Oct 22, 2024 · This class is defined using a generalization of A. Cobham's definition of feasibility for type-1 functions to type-2 functionals. Cobham's ...

Journal of Functional Programming, 11, 2001, pp. 117-153. (PostScript). 1999. Feasibly continuous type-two functionals, B.M.Kapron. computational complexity ...

ThePoly1-continuous functionals have the property that they depend on only a feasible (polynomially bounded) amount of information about their function inputs ( ...

Abstract. We provide a natural characterization of the type two Mehlhorn–Cook–Urquhart basic feasible functionals as the provably total type two functionals ...

Aug 2, 1999 · The complexity of matrix rank and feasible systems of linear equations · Lower bounds for the polynomial calculus and the Gröbner basis algorithm.

We prove that a nite type functional is feasible i it is computable by a bounded typed loop program. 2 Examples. A type 0 functional is just a natural number. A ...