LLMs versus the Halting Problem: Characterizing Program Termination Reasoning 文章

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? We evaluate frontier LLMs on a diverse set of C programs from the International Competition on Software Verification (SV Comp) 2025. Our results show that GPT-5 and Claude Sonnet 4.5 achieve scores comparable to top ranked verification tools (with test time scaling).