Non-deterministic Characterisations

TL;DR

This paper extends Jones' characterization of complexity classes using cons-free programming to include non-determinism and pattern-matching, revealing the increased power of non-determinism in higher-order settings and establishing a hierarchy under restrictions.

Contribution

It generalizes Jones' results to non-deterministic and pattern-matching settings, demonstrating the power of non-determinism and establishing a hierarchy with restrictions.

Findings

Non-determinism significantly increases computational power in higher-order programming.

A hierarchy similar to Jones' can be established with appropriate restrictions.

The results include a parallel characterization of complexity classes with non-determinism.

Abstract

In this paper, we extend Jones' result -- that cons-free programming with $k^{th}$-order data and a call-by-value strategy characterises EXP$^k$TIME -- to a more general setting, including pattern-matching and non-deterministic choice. We show that the addition of non-determinism is unexpectedly powerful in the higher-order setting. Nevertheless, we can obtain a non-deterministic parallel to Jones' hierarchy result by appropriate restricting rule formation.