Context Free Languages

Productions:	A → α
	A ∈ N
	α ∈ V* em i.e. any string

• Since left-hand-side of each production is a single nonterminal, every derivation is a tree.

• Many good parsers are known. Parsing requires a recursive program, or equivalently, a stack for temporary storage.

• Parsing time is at worst O(n³) , though programming languages are commonly O(n) .

• Used for language elements that can contain themselves, e.g.,
  • Arithmetic expressions can contain subexpressions: A + B * (C + D) .

  • A noun phrase can contain a prepositional phrase, which contains a noun phrase:
    a girl with a hat on her head.

• Any language that requires counting must be at least context free: aⁿbⁿ , balanced parentheses.