Large language models (LLMs) are used as post hoc explainers of sequential decision-making policies, producing natural-language explanations of why an action was chosen. However, LLMs often generate plausible but incorrect statements, and no existing approach systematically tests whether such explanations are faithful to the underlying environment. Two classic software testing challenges stand in the way: there is no oracle for the correctness of an explanation, and the test inputs, natural language queries about a policy's behavior, lack the structure needed for systematic test case generation. We address both. Probabilistic model checking provides the test oracle, computing exact reference results against which LLM answers are graded automatically. A taxonomy of post hoc query categories structures the input space around the environment-level facts from which policy explanations are composed; test cases generated from it are prioritized by question-specific diagnostic difficulty scores. Across seven MDP environments, the testing separates three open-weight LLMs: a reasoning model passes 85% of test cases, a mid-size model 70%, and a 1B model falls below the random baseline, while prioritization surfaces significantly harder cases than random selection. Our results indicate how trustworthy LLM-generated explanations are in model-free settings, where the same LLMs are used but no oracle exists to verify them.
Large language models (LLMs) are increasingly used for a range of software, hardware and human-centered security tasks. Consequently, LLM performance on security tasks is an active area of measurement and research, often with a focus on identifying areas in which LLM security "knowledge" may be insufficient. Popular strategies for identifying LLM security knowledge gaps include building corpora of challenge questions or task benchmarks, strategies that require substantial manual work and security expertise to design and execute. We introduce a partially-automated method for assessing LLM knowledge of a security area. The method uses authoritative information from Consumer Protection Agencies (CPAs) to identify instability in LLM responses that can be indicative of knowledge gaps. We demonstrate the method for 2 security topics, identity theft and impostor scams, and 5 LLMs in 2 leading LLM families, Gemini and GPT, using publicly available information about identity theft and impostor scams from 6 CPAs. The method distinguishes between models that have and don't have sufficient knowledge to accurately identify the security topics in text narratives.