Production (computer science) in the context of "L-system"

A formal grammar is a set of symbols and the production rules for rewriting some of them into every possible string of a formal language over an alphabet. A grammar does not describe the meaning of the strings — only their form.

In applied mathematics, formal language theory is the discipline that studies formal grammars and languages. Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas.

In theoretical computer science and formal language theory, a regular grammar is a grammar that is right-regular or left-regular.While their exact definition varies from textbook to textbook, they all require that

• all production rules have at most one non-terminal symbol;
• that symbol is either always at the end or always at the start of the rule's right-hand side.

Every regular grammar describes a regular language.

In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context.In particular, in a context-free grammar, each production rule is of the form

with ${\displaystyle A}$ a single nonterminal symbol, and ${\displaystyle \alpha }$ a string of terminals and/or nonterminals (${\displaystyle \alpha }$ can be empty). Regardless of which symbols surround it, the single nonterminal ${\displaystyle A}$ on the left hand side can always be replaced by ${\displaystyle \alpha }$ on the right hand side. This distinguishes it from a context-sensitive grammar, which can have production rules in the form ${\displaystyle \alpha A\beta \rightarrow \alpha \gamma \beta }$ with ${\displaystyle A}$ a nonterminal symbol and ${\displaystyle \alpha }$, ${\displaystyle \beta }$, and ${\displaystyle \gamma }$ strings of terminal and/or nonterminal symbols.

In formal languages, terminal and nonterminal symbols are parts of the vocabulary under a formal grammar. Vocabulary is a finite, nonempty set of symbols. Terminal symbols are symbols that cannot be replaced by other symbols of the vocabulary. Nonterminal symbols are symbols that can be replaced by other symbols of the vocabulary by the production rules under the same formal grammar.

A formal grammar defines a formal language over the vocabulary of the grammar.

A context-sensitive grammar (CSG) is a formal grammar in which the left-hand sides and right-hand sides of any production rules may be surrounded by a context of terminal and nonterminal symbols. Context-sensitive grammars are more general than context-free grammars, in the sense that there are languages that can be described by a CSG but not by a context-free grammar. Context-sensitive grammars are less general (in the same sense) than unrestricted grammars. Thus, CSGs are positioned between context-free and unrestricted grammars in the Chomsky hierarchy.

A formal language that can be described by a context-sensitive grammar, or, equivalently, by a noncontracting grammar or a linear bounded automaton, is called a context-sensitive language. Some textbooks actually define CSGs as non-contracting, although this is not how Noam Chomsky defined them in 1959. This choice of definition makes no difference in terms of the languages generated (i.e. the two definitions are weakly equivalent), but it does make a difference in terms of what grammars are structurally considered context-sensitive; the latter issue was analyzed by Chomsky in 1963.