arXiv:2601.18987v5 Announce Type: replace Abstract: Determining whether a program terminates is a central problem in computer science. Turing's Halting Problem established termination as undecidable, showing that no algorithm can universally determine termination for all programs and inputs. Hence, verification tools approximate termination, sometimes failing to prove or disprove; these tools rely on problem specific architectures, and are usually tied to particular programming languages. Recent advances in LLMs raise a natural question: To what extent can they reason about program termination
The rapid advancement and widespread adoption of Large Language Models (LLMs) necessitate a rigorous examination of their capabilities and limitations in complex computational reasoning tasks such as program termination.
Understanding LLMs' ability to reason about program termination provides crucial insights into their potential for advanced automated software development, verification, and debugging, which are fundamental to virtually all modern technological infrastructure.
The focus expands from traditional algorithmic approaches for program verification to exploring the emergent reasoning capabilities of LLMs, potentially leading to new paradigms in software tooling and engineering.
- · AI/ML researchers
- · Software development companies
- · Verification tool developers
- · Traditional symbolic verification tool vendors (if LLMs prove superior)
LLMs demonstrate varying levels of success in tackling the Halting Problem and related program termination reasoning.
This capability, if sufficiently robust, could lead to significant advancements in automated code generation, error detection, and formal program verification.
The integration of LLM-based termination reasoning into development pipelines could drastically reduce software bugs and accelerate the development of complex, reliable systems, potentially impacting sectors from aerospace to finance.
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