$\forall$uto$\exists$val: Autonomous Assessment of LLMs in Formal Synthesis and Interpretation Tasks

This paper presents $\forall$uto$\exists$val, a new approach for scaling LLM assessment in translating formal syntax -- such as first-order logic, regular expressions, etc -- to natural language (interpretation) or vice versa (compilation), thereby facilitating their use in applications such as generating/explaining logic and control flow for programs etc. Existing approaches for LLM assessment in these areas require labor-intensive ground-truth creation, the availability of which undermines the separation of training and test sets. Furthermore, such datasets typically include relatively few hand-coded test cases over which LLM accuracy is determined, thus making them inadequate for determining the safety or correctness of their generated outputs. We introduce a new approach that utilizes context-free grammars (CFGs) to generate out-of-distribution datasets on the fly and perform closed-loop testing of LLM capabilities using formal verifiers to guarantee the correctness of LLM outputs without any human intervention. We release our dataset and benchmark as open-source code at \url{https://github.com/AAIR-lab/auto-llm-assessment}. We also conduct an assessment of several SOTA closed and open-source LLMs to showcase the feasibility and scalability of this paradigm. Our experiments reveal that SOTA LLMs are unable to solve the formal translation task adequately.