Formal grammar

A formal grammar is a mathematical system of symbols and production rules that generates or specifies the strings belonging to a language.

Terminal symbol: A symbol that can appear in a string generated by a grammar and cannot be replaced by a production rule. Terminals form the finished strings that the grammar specifies.
Chomsky normal form: A restricted form of context-free grammar whose productions have tightly specified shapes. This normal form makes the structure of context-free derivations easier to analyze.
Finite-state automaton: A computational model with finitely many states that recognizes regular languages. Automata recognize languages through state transitions rather than production-based derivations.
Compiler: A program that translates source code into another representation or executable form. Compiler front ends commonly use grammars to describe and parse source syntax.
Noam Chomsky: An American linguist and cognitive scientist who developed influential theories of generative grammar. His work made formal grammars central to modern linguistic theory.
Nonterminal symbol: A symbol that production rules can replace with other symbols during a derivation. Nonterminals mark structures that rules expand into strings.
Parse tree: A tree showing how a string can be derived from a grammar's start symbol. Its branches make the hierarchical structure of a grammar's rule applications explicit.
Regular expression: A notation that describes regular languages using operations such as union, concatenation, and repetition. Regular expressions specify the same language class as regular grammars in a different form.
Backus–Naur form: A notation for writing production rules that define programming-language syntax. It presents grammar rules in a form used in many language specifications.
Emil Post: A mathematician whose work included formal systems, computability, and production-based rewriting systems. Post systems provide a related historical model of rule-governed symbol generation.

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