formal language theory
Automata also provide an abstract model for computation itself, thus linking formal language theory with the study of computability and complexity. Other issues in formal language theory include decidability of properties of languages, closure properties of language classes, and characterizations of language classes (see Dyck language). An example of a long-standing open question is the decidability of equivalence for deterministic pushdown automata.
The subject has been extended beyond the study of strings to include the study of sets of trees, graphs, and infinite strings, resulting in many more applications.
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