Can AI Predict Program Termination? LLMs Enter the Fray

The Halting Problem has long stood as a cornerstone challenge in computer science, ever since Turing's brilliant mind declared it undecidable. No algorithm can universally predict whether any given program will stop or run indefinitely. This foundational limitation has meant that our best tools for program verification rely on approximations, and often they're tied to specific programming languages.

The Role of Large Language Models

Enter large language models (LLMs). As these AI behemoths become more sophisticated, a tantalizing question emerges: could they reliably predict program termination? Recent evaluations have thrown new light on this. By testing LLMs like GPT-5 and Claude Sonnet-4.5 on a variety of programs from the Termination category of the International Competition on Software Verification (SV-Comp) 2025, some intriguing patterns have emerged.

These LLMs aren't just doing well, they're nearly top-tier. Using test-time scaling, they rank just behind the leading tool, with Code World Model (CWM) not far behind, trailing the second spot. However, despite their predictive prowess, LLMs frequently stumble when asked to produce a valid witness as proof of termination. As program length and complexity rise, their performance notably wanes. Isn't it time we ask if relying on LLMs for such tasks is truly wise, especially when they can't always substantiate their predictions?

Why It Matters

Let's apply the standard the industry set for itself. If LLMs can't consistently handle increasing complexity, what's their true value in program verification? The hope is that these insights spur further research, not just into program termination, but into the broader capabilities of LLMs to tackle undecidable problems. The burden of proof sits with the team, not the community. Until then, it seems we're left with a tool that shows promise but falls short of transforming the verification landscape.

Nevertheless, the strides LLMs have made are commendable. They indicate a potential shift in how we approach certain computational problems. But before we pop the champagne, let's remember: skepticism isn't pessimism. It's due diligence. We must demand transparency and accountability from these AI systems if they're to be integrated into our tech ecosystems.