2023/09/11 by Qingxiu Dong, Li Dong, Dong, Qingxiu +11 · 5 voices
Computer Science · #Artificial Intelligence (cs.AI) #Computation and Language (cs.CL) #FOS: Computer and information sciences #cs.AI #cs.CL
paper · pdf · doi:10.48550/arxiv.2309.05689
In this work, we use large language models (LLMs) to augment and accelerate research on the P versus NP problem, one of the most important open problems in theoretical computer science and mathematics. Specifically, we propose Socratic reasoning, a general framework that promotes in-depth thinking with LLMs for complex problem-solving. Socratic reasoning encourages LLMs to recursively discover, solve, and integrate problems while facilitating self-evaluation and refinement. Our pilot study on the P vs. NP problem shows that GPT-4 successfully produces a proof schema and engages in rigorous reasoning throughout 97 dialogue turns, concluding "P ≠ NP", which is in alignment with (Xu and Zhou, 2023). The investigation uncovers novel insights within the extensive solution space of LLMs, shedding light on LLM for Science.