Noncontracting grammar

A monotone grammar (also nichtverkürzende grammar or limited grammar) is a formal grammar that includes only production rules whose right side is not shorter than the left side. A derivation step in a monotone grammar does not shorten the sentence to be derived form.

Definition

Formally, a monotonic grammar is defined as a 4- tuple with

• Nonterminal symbols
• Terminal symbols symbol set

If communication is allowed for monotonic grammars the exception rule, if not occur in any right-hand side of a rule, the monotone grammars generate exactly the context-sensitive languages ​​and are thus equivalent to the context-sensitive grammars.

Example

The grammar, and:

Generates the language.