A new function algebra of EXPTIME functions by safe nested recursion

TL;DR

This paper introduces a novel function algebra that characterizes EXPTIME functions using a safe nested recursion scheme, extending Bellantoni and Cook's polynomial-time framework.

Contribution

It presents a new safe nested recursion scheme that captures exponential-time computable functions, expanding the scope of function algebra characterizations.

Findings

Defines a safe nested recursion scheme for EXPTIME functions

Provides a characterization of exponential-time computable functions

Extends the Bellantoni-Cook framework to higher complexity classes

Abstract

Bellantoni and Cook have given a function-algebra characterization of the polynomial-time computable functions via an unbounded recursion scheme which is called safe recursion. Inspired by their work, we characterize the exponential-time computable functions with the use of a safe variant of nested recursion.