Theory of Automata

Context Free Language

Context free grammar has production rules which are used to generate context free language. Context free languages are accepted by Push down automata (PDA).

  • All Regular languages and CFL are accepted by PDA.
  • For all context free languages, there must be one comparison in terminals of string e L= {anbn n>=0}

A context Free Grammar (CFG) is a 4-tuple such that

G = (V , T , P , S)


  • V = Finite set of variables / non-terminal symbols. These are denoted by capital letters.
  • T = Finite set of terminal symbols . these are use to replace the variables. These are denoted by lower case letters.
  • P = Production rules are used to generate CFL. i.e. A → α , where A ∈ V and α ∈ (V ∪ T)*. Keep in mind left side must contain only one variable but right side ((V ∪ T)*) may contain more than one terminals and non-terminals.
  • S = Start symbol

Example Of Context Free Language

Consider a grammar G = (V , T , P , S) where-

  • V = { S }
  • T = { a , b }
  • P = { S → aSbS , S → bSaS , S → ∈ }
  • S = { S }

Above production rules generates the strings having equal number of a’s and b’s. it is an example of context free language

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