Given a descriptive theory of language structure, we can distinguish its 'weak generative capacity' from its 'strong generative capacity' in the following way. Let us say that a grammar 'weakly generates' a set of sentences and that it 'strongly generates' a set of structural descriptions (recall that each structural description uniquely specifies a sentence, but not necessarily conversely) [...] Suppose that the linguistic theory T provides the class of grammars G1, G2,..., where Gi weakly generates the language Li and strongly generates the system of structural descriptions Σi. Then the class {L1, L2,...} constitutes the 'weak generative capacity' of T and the class {Σ1, Σ2...} constitutes the 'strong generative capacity' of T.
- Chomsky (1969), Pag. 60