Regulated rewriting is a specific area of formal languages studying grammatical systems which are able to take some kind of control over the production applied in a derivation step. For this reason, the grammatical systems studied in Regulated Rewriting theory are also called "Grammars with Controlled Derivations". Among such grammars can be noticed:
A Matrix Grammar, , is a four-tuple where
1.- is an alphabet of non-terminal symbols
2.- is an alphabet of terminal symbols disjoint with
3.- is a finite set of matrices, which are non-empty sequences , with , and , where each , is an ordered pair being these pairs are called "productions", and are denoted . In these conditions the matrices can be written down as
4.- S is the start symbol
Let be a matrix grammar and let the collection of all productions on matrices of . We said that is of type i according to Chomsky's hierarchy with , or "increasing length" or "linear" or "without -productions" if and only if the grammar has the corresponding property.
The classic example
- Note: taken from Abraham 1965, with change of nonterminals names
The context-sensitive language is generated by the where is the non-terminal set, is the terminal set, and the set of matrices is defined as , , , .
Time Variant Grammars
A Time Variant Grammar is a pair where is a grammar and is a function from the set of natural numbers to the class of subsets of the set of productions.
A Programmed Grammar is a pair where is a grammar and are the success and fail functions from the set of productions to the class of subsets of the set of productions.
Grammars with regular control language
A Grammar With Regular Control Language, , is a pair where is a grammar and is a regular expression over the alphabet of the set of productions.
A naive example
Consider the CFG where is the non-terminal set, is the terminal set, and the productions set is defined as being , , , , and . Clearly, . Now, considering the productions set as an alphabet (since it is a finite set), define the regular expression over : .
Combining the CFG grammar and the regular expression , we obtain the CFGWRCL which generates the language .
Besides there are other grammars with regulated rewriting, the four cited above are good examples of how to extend context-free grammars with some kind of control mechanism to obtain a Turing machine powerful grammatical device.
 Salomaa, Arto (1973) Formal languages Academic Press, ACM monograph series
 Rozenberg, G.; Salomaa, A. (eds.) 1997 Handbook of formal languages Berlin; New York : Springer ISBN 3-540-61486-9 (set) (3540604200 : v. 1; 3540606483 : v. 2; 3540606491: v. 3)
 Dassow, Jurgen; Paun, G. 1990 Regulated Rewriting in Formal Language Theory ISBN 0387514147. Springer-Verlag New York, Inc. Secaucus, NJ, USA Pages: 308. Medium: Hardcover.
 Abraham, S. 1965. "Some questions of language theory", Proceedings of the 1965 International Conference On Computational Linguistics, pp 1 – 11, Bonn, Germany Available at: