First & Follow Question

Question

is it correct?

Comments

first(E) = { }

first(T) = { }

rest all are correct.

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@joshi_nitish is it possible that we have first set as empty set?

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yes possible,,,but follow() does not have { } becoz they have atleast $

Answer 1

The grammar is left recursive.

Remove left recursion and then find FIRST and FOLLOW.

Comments

There is change in question my mistake its

E =E+T/T

T=T*F/F

F=(E) /Id my answer is of this question I mentioned

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I solved this qusetion and based on that found given grammar is ll1. I did without removing left recursion as I am comfortable with it is it correct?

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@Pranav Madhani You can find first and follow without removing left recursion. But LL1 grammar is never left recursive. The production with left recursion will be definitely in two entries.

Answer 2

Taking gammer from your comment

E -> E+T | T
T -> T*F | F
F -> (E) | id

Remove left recursion first

E -> TE'
E'  -> +TE' | $\epsilon$
T -> FT'
T' -> *FT' | $\epsilon$
F -> (E) | id

First (E) = { (, id }          Follow (E ) = { dollar, ), + }
First (T) = { (, id }          Follow (T) =  { dollar, +,*, ) }
First (F) = { (, id }          Follow (F) = { dollar, +, *, ) }

All your answers are correct.

Comments

@`JEET after changing the grammar FOLLOW(E) will only have {$, )}.

And if you don't change it then Follow(E) = {$, ), +}.

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But answer should not be different?

As on removing the left recursion, the grammar is still the same only but just the left recursion is removed?

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Is this correct one ?

Answer 3

@`JEET I had made program for SLR1 and CLR1 last sem, there I had to find the first and follow without changing the grammar. That's why I used this approach.

Taking grammar from the comment 

E -> E+T | T
T -> T*F | F
F -> (E) | id

If a production symbol has left recursion then ignore for the first time and find FIRST for all the other productions of that symbol. And if that symbol contains EPSILON then find the FIRST of the production which had left recursion.

Example: 

First(E) = FIRST(T) = FIRST(F) = { (, id }

If F had EPSILON,then check again the first of E+T, then you will even get + in the FIRST(E).

Finding follow is simple.

Comments

@`JEET strings generated by the grammar will not be different, but the means of generating them will change. In a way, you are changing the grammar without affecting its functionality, but its attributes can change (first and follow).

first and follow are not the answer of a grammar, strings generated by the grammar is the answer.

See the above solution.