Question

Given the following grammar:

A -> A ; B

A -> B

                                       B -> B , C

                                       B -> C

                                       C -> ( A )

                                       C -> a

rewrite the grammar to avoid left recursion

For the rewritten grammar of question , Compute First, Follow, and nullable.

Answer 1

The given grammar is :

A -> A ; B

A -> B

B -> B , C

B -> C

C -> ( A )

C -> a

The given grammar is converted to the following equivalent grammar without left recursion :

A -> B A '

A ' -> ; B A ' | ε

B -> C B '

B ' -> , C B ' | ε

C -> ( A )

C -> a

The First of all the variables is computed as follows :

First(A) = { ( a }

First(A') = { ; ε }

First(B) = { ( a }

First(B') = { , ε }

First(C) = { ( a }

The Follow of all the variables is computed as follows :

Follow(A) = { $  ) }

Follow(A') =   { $  ) }

Follow(B) = { ; $  ) }

Follow(B') = { ; $  ) }

Follow(C) = { , ; $  ) }

The nullable variables refer to the variables which yield ε on 0 or more steps.

The nullable variables are A ' and B ' .