Achieving accessibility compliance is extremely important for many government agencies and businesses who wish to improve services for their consumers. With the growing reliance on dynamic web applications many organizations are finding it difficult to implement accessibility standards, often due to the inability of current automated testing tools to test the stateful environments created by dynamic web applications. In this paper, we present mathematical foundations and theory for the Demodocus framework and prototype, and outline its approach to using web science, web crawling,and accessibility testing to automatically navigate and test interactive content for accessibility. Our approach simulates the page interactions of users with and without disabilities, and compares graphs of reachable states from these simulations to determine both the accessibility and the difficulty of content access for these different users.