Phrase Structure Grammar

A grammar describes the structure of the sentences of a language in terms of components, or phrases. The mathematical description of phrase structure grammars is due to Chomsky.[See, for example, Aho, A. V. and Ullman, J. D., The Theory of Parsing, Translation, and Compiling, Prentice-Hall, 1972; Hopcroft, J. E. and Ullman, J. D., Formal Languages and their Relation to Automata, Addison-Wesley, 1969.]

Formally, a Grammar is a four-tuple G = (T, N, S, P) where:

• T is the set of terminal symbols or words of the language.

• N is a set of nonterminal symbols or phrase names that are used in specifying the grammar. We say V = T ∪ N is the vocabulary of the grammar.

• S is a distinguished element of N called the start symbol.
• P is a set of productions, P ⊆ V^*NV^* X V^* . We write productions in the form a → b where a is a string of symbols from V containing at least one nonterminal and b is any string of symbols from V.