Question

How can I convert some regular language to its equivalent Context Free Grammar?
Is it necessary to construct the DFA corresponding to that regular expression or is there some rule for such a conversion?

For example, consider the following regular expression

01+10(11)^*

How can I describe the grammar corresponding to the above RE?

Answer 1

• Change A+B to grammar

  G -> A
  G -> B
  

• Change A* to

  G -> (empty)
  G -> A G
  

• Change AB to

  G -> AB
  

and proceed recursively on A and B. Base cases are empty language (no productions) and a single symbol.

In your case

 A -> 01
 A -> 10B
 B -> (empty)
 B -> 11B

If the language is described by finite automaton:

• use states as nonterminal symbols
• use language as set of terminal symbols
• add a transition p -> aq for any transition p -> q on letter a in the original automaton
• use initial state as initial symbol in the grammar