Busy Beaver Machines and the Observant Otter Heuristic (or How to Tame Dreadful Dragons)

TL;DR

This paper introduces the observant otter heuristic to evaluate large busy beaver machines, providing a framework and empirical evidence for addressing the non-computable nature and size of these problems.

Contribution

It presents a new heuristic and framework for analyzing busy beaver machines, enabling evidence collection for machines with extremely large execution steps.

Findings

The observant otter heuristic effectively evaluates known monster machines.

The framework aids in providing evidence for maximality claims.

Empirical results demonstrate the heuristic's efficiency on large machines.

Abstract

The busy beaver is a well-known specific example of a non-computable function. Whilst many aspect of this problem have been investigated, it is not always easy to find thorough and convincing evidence for the claims made about the maximality of particular machines, and the phenomenal size of some of the numbers involved means that it is not obvious that the problem can be feasibly addressed at all. In this paper we address both of these issues. We discuss a framework in which the busy beaver problem and similar problems may be addressed, and the appropriate processes for providing evidence of claims made. We also show how a simple heuristic, which we call the observant otter, can be used to evaluate machines with an extremely large number of execution steps required to terminate. We also show empirical results for an implementation of this heuristic which show how this heuristic is effective for all known `monster' machines.