Computational Reasoning of Large Language Models

Abstract

With the rapid development and widespread application of Large Language Models (LLMs), multidimensional evaluation has become increasingly critical. However, current evaluations are often domain-specific and overly complex, limiting their effectiveness as cross-domain proxies for core capabilities. To address these limitations and enable a unified and simple evaluation framework, an ideal proxy task should target a basic capability that generalizes across tasks and is independent of domain-specific knowledge. Turing machine provides a powerful theoretical lens by reducing complex processes to basic, domain-agnostic computational operations. This perspective offers a principled framework for evaluating basic computational abilities essential to a wide range of tasks. Motivated by this abstraction, we introduce \textbf{Turing Machine Bench}, a benchmark designed to assess the ability of LLMs to \textbf{strictly follow rules} and \textbf{accurately manage internal states} for multi-step, referred to as \textbf{computational reasoning}. TMBench incorporates four key features: self-contained and knowledge-agnostic reasoning, a minimalistic multi-step structure, controllable difficulty, and a solid theoretical foundation based on Turing machine. Empirical results demonstrate that TMBench serves as an effective proxy for evaluating computational reasoning on representative LLMs. It produces clear step-wise accuracy curves, revealing LLMs' ability to execute multi-step reasoning processes. By analyzing performance trends across TMBench and established reasoning benchmarks, we find strong correlations with real-world tasks, bridging real-task evaluation with basic ability assessment. These findings suggest that TMBench holds potential as a cross-domain dimension for evaluating reasoning in LLMs. Code and data are available at \href{https://github.com/HaitaoWuTJU/Turing-Machine-Bench}{Repo}.