  In the realm of embodied artificial intelligence, the reasoning capabilities
of Large Language Models (LLMs) play a pivotal role. Although there are
effective methods like program-of-thought prompting for LLMs which uses
programming language to tackle complex reasoning tasks, the specific impact of
code data on the improvement of reasoning capabilities remains under-explored.
To address this gap, we propose complexity-impacted reasoning score (CIRS),
which combines structural and logical attributes, to measure the correlation
between code and reasoning abilities. Specifically, we use the abstract syntax
tree to encode the structural information and calculate logical complexity by
considering the difficulty and the cyclomatic complexity. Through an empirical
analysis, we find not all code data of complexity can be learned or understood
by LLMs. Optimal level of complexity is critical to the improvement of
reasoning abilities by program-aided prompting. Then we design an
auto-synthesizing and stratifying algorithm, and apply it to instruction
generation for mathematical reasoning and code data filtering for code
generation tasks. Extensive results demonstrates the effectiveness of our
proposed approach. Code will be integrated into the EasyInstruct framework at
https://github.com/zjunlp/EasyInstruct.
