Reverse Mathematical Bounds for the Termination Theorem

TL;DR

This paper explores the logical strength of the Termination Theorem for transition-based programs within Reverse Mathematics, aiming to extract bounds on program termination by analyzing the theorem's foundational requirements.

Contribution

It provides a reverse mathematical analysis of the Termination Theorem, linking classical termination proofs to their logical strength and potential bounds.

Findings

Identifies the logical strength needed for the Termination Theorem

Connects classical termination proofs to Reverse Mathematics frameworks

Extracts bounds on program termination from logical analysis

Abstract

In 2004 Podelski and Rybalchenko expressed the termination of transition-based programs as a property of well-founded relations. The classical proof by Podelski and Rybalchenko requires Ramsey's Theorem for pairs which is a purely classical result, therefore extracting bounds from the original proof is non-trivial task. Our goal is to investigate the termination analysis from the point of view of Reverse Mathematics. By studying the strength of Podelski and Rybalchenko's Termination Theorem we can extract some information about termination bounds.