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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, PrenticeHall, 1972; Hopcroft, J. E. and Ullman, J. D.,
Formal Languages and their Relation to Automata, AddisonWesley,
1969.]
Formally, a Grammar is a fourtuple
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.