Title: Nondeterministic Polynomial-time Problem Challenge: An Ever-Scaling Reasoning Benchmark for LLMs
Primary area: datasets and benchmarks
Keywords: LLM Reasoning, Computational Complexity, Evaluation

Abstract: Reasoning is the fundamental capability of large language models (LLMs).
Due to the rapid progress of LLMs, there are two main issues of current benchmarks: i) these benchmarks can be *crushed* in a short time (less than 1 year), and ii) these benchmarks may be easily *hacked*. To handle these issues, we propose the **ever-scalingness** for building the benchmarks which are scaling over complexity, instance, oversight and coverage. This paper presents Nondeterministic Polynomial-time Problem Challenge (**NPPC**) , an ever-scaling reasoning benchmark for LLMs. Specifically, the **NPPC** has three main modules: i) *npgym*,
which provides a unified interface of 25 well-known NP-complete problems and can generate any number of instances with any levels of complexities, ii) *npsolver*, which provides a unified interface to evaluate the problem instances with both online and offline models via APIs and local deployments, respectively, and iii) *npeval*, which provides the comprehensive and ready-to-use tools to analyze the performances of LLMs over different problems, the number of tokens, the aha moments, the reasoning errors and the solution errors. Extensive experiments over widely-used LLMs demonstrate: i) **NPPC** can successfully decrease the performances of advanced LLMs to below 10%, demonstrating that **NPPC** is not crushed by current models, ii) DeepSeek-R1, Claude-3.7-Sonnet, and o1/o3-mini are the most powerful LLMs, where DeepSeek-R1 can outperform Claude-3.7-Sonnet and o1/o3-mini in most NP-complete problems considered, and iii) the numbers of tokens, aha moments in the advanced LLMs, e.g., Claude-3.7-Sonnet and DeepSeek-R1, are observed first to increase and then decrease when the problem instances become more and more difficult. Through continuously scaling analysis, **NPPC** can provide critical insights into LLMs' reasoning capabilities, exposing fundamental limitations and suggesting future directions for further improvements.

TL;DR: We propose an ever-scaling reasoning benchmark NPPC, which is uncrushable and unhackable for LLMs.