Abstract
AbstractThe class of basic feasible functionals ($$\texttt{BFF}$$
BFF
) is the analog of $$\texttt{FP}$$
FP
(polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments. $$\texttt{BFF}$$
BFF
can be defined through Oracle Turing machines with running time bounded by second-order polynomials. On the other hand, higher-order term rewriting provides an elegant formalism for expressing higher-order computation. We address the problem of characterizing $$\texttt{BFF}$$
BFF
by higher-order term rewriting. Various kinds of interpretations for first-order term rewriting have been introduced in the literature for proving termination and characterizing (first-order) complexity classes. In this paper, we consider a recently introduced notion of cost–size interpretations for higher-order term rewriting and see definitions as ways of computing functionals. We then prove that the class of functionals represented by higher-order terms admitting a certain kind of cost–size interpretation is exactly $$\texttt{BFF}$$
BFF
.
Publisher
Springer Nature Switzerland
Cited by
2 articles.
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1. Declassification Policy for Program Complexity Analysis;Proceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science;2024-07-08
2. On Basic Feasible Functionals and the Interpretation Method;Lecture Notes in Computer Science;2024