The question asks for two table functions in the Snowflake Information Schema that retrieve information about directory tables. Based on the community discussion and Snowflake documentation references provided, AUTO_REFRESH_REGISTRATION_HISTORY (A) retrieves the history of data files registered in metadata and credits billed, while STAGE_DIRECTORY_FILE_REGISTRATION_HISTORY (E) retrieves metadata history for directory tables including refresh errors. These are specifically designed for directory tables. Option C (EXTERNAL_TABLE_FILES) is for external tables, not directory tables, and option B (EXTERNAL_TABLE_FILE_REGISTRATION_HISTORY) is not a standard Snowflake function. Option D (MATERIALIZED_VIEW_REFRESH_HISTORY) is unrelated to directory tables. The consensus (78% AE vs 22% CE) and higher upvotes support AE as correct.