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Did the Problem Actually Get Harder? Testing LLMs on Paired P and NP-Complete Problems Hardened by Adversarial Multi-Agent Rewriting

Nurul Labib Sayeedi, Md. Faiyaz Abdullah Sayeedi, Zabir Al Nazi, Mahbub E. Sobhani, Shubhashis Roy Dipta · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30103 · cited by 0 works (OpenAlex) · open-access PDF

Indonesian

Banyak masalah NP-complete (NPC) memiliki kembar polynomial-time (P) yang berbeda dalam satu rincian struktural, seperti 3- vs 2-colouring a graph. Sebuah model yang alasan daripada mengingatkan harus memperhatikan sisi mana dari batas ini masalah jatuh, namun referensi yang ada baik memperbaiki formulasi setiap tugas atau mengabaikan kelas kompleksitasnya, sehingga mereka tidak dapat memisahkan keduanya. Kami memperkenalkan P2NPCBench, benchmark dari 12 keluarga masalah di mana setiap masalah NPC dikombinasikan dengan P kembar yang ditempatkan di atas permukaan yang sama. Untuk menghapus petunjuk buku teks yang memungkinkan pengingat, kami membangunnya dengan AgentGAN, kerangka multi-agen yang berlawanan di mana generator menulis ulang setiap pernyataan sampai panel model kode beku gagal, sementara gateway validitas yang dapat dieksekusi menjaga setiap jawaban tertulis

Machine translation (Meta M2M100); the English original follows.

Abstract

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. The result is 2,114 hardened statements with hand-verified reference human solvers. Evaluating 12 proprietary and open-source models, we find that every model scores lower on NPC statements than on their P twins (35.4% vs. 63.8% pass@1), and that 95.1% of model-family pairs fail more often on the NPC side. A tenfold time limit raises NPC accuracy only from 28.5% to 31.9%, so failures stem from wrong or crashing programs rather than slow ones. Hardening also narrows the class gap from 24.8 to 14.6 points, showing that part of the apparent gap reflects familiarity with textbook phrasing rather than complexity class.

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Topics: Adversarial system, Notice, Rewriting, Executable, Task (project management), Computer science

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