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This paper presents $\forall$uto$\exists$$\lor\!\land$L, a novel benchmark for scaling Large Language Model (LLM) assessment in formal tasks with clear notions of correctness, such as truth maintenance in translation and logical reasoning. $\forall$uto$\exists$$\lor\!\land$L is the first benchmarking paradigm that offers several key advantages necessary for scaling objective evaluation of LLMs without human labeling: (a) ability to evaluate LLMs of increasing sophistication by auto-generating tasks at different levels of difficulty; (b) auto-generation of ground truth that eliminates dependence on expensive and time-consuming human annotation; (c) the use of automatically generated, randomized datasets that mitigate the ability of successive LLMs to overfit to static datasets used in many contemporary benchmarks. Empirical analysis shows that an LLM's performance on $\forall$uto$\exists$$\lor\!\land$L is highly indicative of its performance on a diverse array of other benchmarks focusing on translation and reasoning tasks, making it a valuable autonomous evaluation paradigm in settings where hand-curated datasets can be hard to obtain and/or update.

Understanding how robots plan and execute tasks is crucial in today's world, where they are becoming more prevalent in our daily lives. However, teaching non-experts the complexities of robot planning can be challenging. This work presents an open-source platform that simplifies the process using a visual interface that completely abstracts the complex internals of hierarchical planning that robots use for performing task and motion planning. Using the principles developed in the field of explainable AI, this intuitive platform enables users to create plans for robots to complete tasks, and provides helpful hints and natural language explanations for errors. The platform also has a built-in simulator to demonstrate how robots execute submitted plans. This platform's efficacy was tested in a user study on university students with little to no computer science background. Our results show that this platform is highly effective in teaching novice users the intuitions of robot task planning.

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.