Inference of Termination Conditions for Numerical Loops in Prolog

Title: Inference of Termination Conditions for Numerical Loops in Prolog

Abstract: This research paper presents a new approach to termination analysis of numerical computations in logic programs. It discusses the challenges of analyzing such computations due to the non-well-foundedness of integers and introduces a technique that allows overcoming these difficulties. The approach is based on transforming a program in a way that allows integrating and extending techniques originally developed for analyzing numerical computations in the framework of query mapping pairs with the well-known framework of acceptability. This integration not only contributes to the understanding of termination behavior of numerical computations but also allows for a correct analysis of such computations automatically, extending previous work on a constraint-based approach to termination. Finally, the paper discusses possible extensions of the technique, including incorporating general term orderings.

Main Research Question: How can we develop an automated technique for inferring termination conditions for numerical computations in logic programs?

Methodology: The research paper proposes a technique that transforms a program in a way that allows integrating and extending existing techniques for analyzing numerical computations. It discusses the challenges of analyzing such computations due to the non-well-foundedness of integers and introduces a technique that allows overcoming these difficulties.

Results: The paper presents an example that demonstrates the effectiveness of the proposed technique. It shows that the approach can analyze and prove termination for numerical computations, even in cases where existing automated approaches fail.

Implications: The research has implications for the field of logic programming, as it provides a new technique for analyzing termination conditions in numerical computations. This can lead to more reliable and efficient programming, particularly in real-world scenarios where numerical computations are essential. The technique can also be extended to incorporate general term orderings, which could further enhance its applicability and usefulness.

Link to Article: https://arxiv.org/abs/0110034v2 Authors: arXiv ID: 0110034v2