Unary Primitive Recursive Functions

TL;DR

This paper explores new characterizations of primitive recursive functions by restricting recursion schemes and identifying foundational sets, advancing the understanding of their structural properties.

Contribution

It introduces novel characterizations of primitive recursive functions using restricted recursion schemes and closure properties, building on prior foundational work.

Findings

Reduced certain recursion schemes to simpler forms

Characterized one-argument primitive recursive functions via closure properties

Enhanced understanding of the structure of primitive recursive functions

Abstract

In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone in this area. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets.