Did the Problem Actually Get Harder? Testing LLMs on Paired P and NP-Complete Problems Hardened by Adversarial Multi-Agent Rewriting· 问题真的变得更难了吗？

Many NP-complete (NPC) problems have a polynomial-time (P) twin that differs in a single structural detail, such as 3- versus 2-colouring a graph. A model that reasons rather than recalls should notice which side of this boundary a problem falls on, yet existing benchmarks either fix the wording of each task or ignore its complexity class, so they cannot separate the two. We introduce P2NPCBench, a benchmark of 12 problem families in which every NPC problem is paired with a P twin posed over the same surface. To remove the textbook cues that enable recall, we build it with AgentGAN, an adversarial multi-agent framework in which a generator rewrites each statement until a panel of frozen code models fails, while an executable validity gate keeps every rewrite answer- and class-preserving. T