Context Free Grammar
Definition
A context-free grammar G is a quadruple (V, T, P, S), where:
- V is the set of non-terminals. (Non-terminals used in the grammar and they do not appear in strings of the language).
- T is the set of terminals.
- P is the set of productions. All productions in P have the form A → x where A ∈ V and x ∈ (V ∪ T)*.
- S is the start symbol, S ∈ V.
- Every regular grammar is context free, so a regular language is also a context free one.
- Family of regular language is a proper subset of the family of CFLs.
Example:
The grammar G = ({s}, {a, b}, s, p) with productions.
S → aSa
S → bSb
S → λ
is context free A typical derivation in this grammar is
S → aSa → aaSaa → aabSbaa → aabbaa
this, and similar derivations, make it clear that
L(G)={ww R : w ∈ {a, b}*}
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