Examples
An archetypical context-free language is, the language of all non-empty even-length strings, the entire first halves of which are 's, and the entire second halves of which are 's. is generated by the grammar, and is accepted by the pushdown automaton where is defined as follows:
Context-free languages have many applications in programming languages; for example, the language of all properly matched parentheses is generated by the grammar . Also, most arithmetic expressions are generated by context-free grammars.
Read more about this topic: Context-free Language
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