Context-Free Languages

2.1

Concepts: substitution rule (production),variable,terminal,derivation

Definition: a context-free grammar is a 4-tuple(variables, terminals, rules, start variable)

Chomsky normal form:

A ®B, C

A ® a

Theorem:

       Any context free language is generated by a context-free grammar in Chomsky normal form.

 

2.2

A pushdown automaton is a 6-tuple (states, input alphabet, stack alphabet, transition function, start state, accept states)

Theorem

       A language is context free if and only if some pushdown automaton recognizes it.

 

2.3

The pumping lemma for context-free languages

1.    for each i ³ 0 , uvⁱxyⁱz ÎA

2.       |vy| > 0

3.       |vxy| £ p