This paper establishes a formal equivalence between the architectural classes of modern agentic AI systems and the abstract machines of the Chomsky hierarchy. We posit that the memory architecture of an AI agent is the definitive feature determining its computational power and that it directly maps it to a corresponding class of automaton. Specifically, we demonstrate that simple reflex agents are equivalent to Finite Automata, hierarchical task-decomposition agents are equivalent to Pushdown Automata, and agents employing readable/writable memory for reflection are equivalent to TMs. This Automata-Agent Framework provides a principled methodology for right-sizing agent architectures to optimize computational efficiency and cost. More critically, it creates a direct pathway to formal verification, enables the application of mature techniques from automata theory to guarantee agent safety and predictability. By classifying agents, we can formally delineate the boundary between verifiable systems and those whose behavior is fundamentally undecidable. We address the inherent probabilistic nature of LLM-based agents by extending the framework to probabilistic automata that allow quantitative risk analysis. The paper concludes by outlining an agenda for developing static analysis tools and grammars for agentic frameworks.

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