How Well Do LLMs Perform on the Simplest Long-Chain Reasoning Tasks: An Empirical Study on the Equivalence Class Problem

Large Language Models (LLMs) have achieved great improvements in recent years. Nevertheless, it still remains unclear how good LLMs are for reasoning tasks, especially for long-chain ones. In this paper, we evaluate LLMs' performance on the simplest yet long-chain reasoning task, namely the Equivalence Class Problem (ECP), i.e., determining whether two variables are equal given a set of randomly generated equivalence relations. We consider both reasoning and non-reasoning representative LLMs over a large variety of problem instances, ranging over different numbers of variables, connectivity probabilities, prompts, and other factors. The experimental results show that non-reasoning LLMs fail ECP, while reasoning models are significantly better but still struggle to completely solve this problem. Interestingly, considering various connectivity probabilities with a fixed number of variables, we observe that, for non-reasoning models, the hardest problem instances coincide with the phase transition point of ln n/(n-1), suggesting the chaos of the problem; in contrast, for reasoning models, the hardest ones coincide with the biggest diameter, suggesting the reasoning difficulty of the problem.