Generative Capacity
نویسندگان
چکیده
GENERATIVE CAPACITY was introduced by Chomsky (1963) in the context of the theory of formal grammars and automata (→ Finite State Grammars and Languages, → Context Free Grammars and Languages, → Mildly Context Sensitive Grammars and Languages, → Automata Theory). A language is defined as a set of strings over some vocabulary (e.g., a set of sentences over a vocabulary of words). A formal grammar defines a language, in the sense that it provides an abstract mechanism which generates the strings belonging to the language. (We will henceforth use the terminology of grammars; completely parallel formulations are possible in terms of languages accepted by automata within automata theory, or in terms of languages defined by constraint satisfaction within a declarative formalism.) The W[EAK] G[ENERATIVE] C[APACITY] of a grammar is then simply defined as the language generated by the grammar, and the WGC of a class of grammars is defined as the set of languages generated by the grammars in the class. For example, the WGC of a given C[ontext] F[ree] G[rammar] is the C[ontext] F[ree] L[anguage] which it generates, whereas the WGC of the class of CFGs is the set of CFLs. If a theory of grammar is defined as a specification of a set of grammars, then the WGC of that theory is the WGC of the set of grammars thus specified. If a grammar generates strings while at the same time assigning them a structural description of some kind (e.g. a CFG associates each sentence it generates with a tree), then one can define the S[TRONG] G[ENERATIVE] C[APACITY] of the grammar as the set of structural descriptions generated by the grammar. Likewise, the SGC of a class of grammars (or theory) is the set of sets of structural descriptions generated by the grammars in the class: for example, the SGC of the class of CFGs is the set of sets of trees generated by CFGs.
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