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Automata Theory

I've given my answer to 3d. Is it correct? If not, please correct it. Thanks

3. Context-free languages are useful for the definition of programming languages. For example, we have looked at grammars for

3. Context-free languages are useful for the definition of programming languages. For example, we have looked at grammars for defining Lisp and C. (a) Give a context-free language that is not regular, establishing the added power of CFL (b) What language is accepted by the following grammar: (c) Build a context-free grammar for the language (wb w-wR, k 0 a,by (d) Build a context-free grammar for the language of nested parentheses. A left parenthesis should always precede its matching right parenthesis. Two strings in this language are () and (00)0. This grammar could be used to check the syntactic correctness of a Lisp expression.
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Answer #1

3d)

      E --> EE | LER | ε

      L --> (

      R --> )

EE is used to produce parenthesis side by side.

LER is used to produce recursive parenthesis.

symbol L is used to produce left parenthesis.

symbol R is used to produce right parenthesis.

ε - empty string.

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