Automata theory is the branch of theoretical computer science that studies abstract computing machines (automata) and the classes of formal languages they can recognise. It classifies machines such as finite-state automata, pushdown automata, and Turing machines by their computational power, establishing a hierarchy that defines what problems are decidable. The theory provides the formal foundations for compiler design, regular expressions, protocol verification, and model checking.
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- The Chomsky hierarchy links automata classes to grammar classes: finite automata recognise regular languages, pushdown automata context-free languages, and Turing machines recursively enumerable languages. These results bound the expressiveness and decidability of computation, informing parsing, verification, and circuit design.