Proving programs terminate using well orderings, Ramsey Theory, and Matrices

TL;DR

This paper explores methods to prove program termination using well orderings, Ramsey Theory, and matrices, highlighting their application in real program checkers to ensure programs do not run infinitely regardless of user input.

Contribution

It introduces a comprehensive approach combining well orderings, Ramsey Theory, and matrices for termination proofs, demonstrating their practical relevance in program verification.

Findings

Techniques are used by real program checkers.

Methods effectively prove termination regardless of user input.

The approach unifies different mathematical tools for program analysis.

Abstract

Many programs allow the user to input data several times during its execution. If the program runs forever the user may input data infinitely often. A program terminates if it terminates no matter what the user does. We discuss various ways to prove that program terminates. The proofs use well orderings, Ramsey Theory, and Matrices. These techniques are used by real program checkers.