Find if the grammar is LL(1)

Question

Consider the grammar:
S -> ab | ac
Is this grammar LL(1)?

My try : I tried doing the left-factoring and create the LL(1) table and found that the grammar is LL(1), but the answer is given to be not LL(1).

Answer 1

First (ab) = a = First (ac) thats why it is not LL(1). Because it contain left factoring.

Suppose we derive ab and choose production S-> ac insteed of S-> ab . then we get error message string not present but actualy it is present .So Remove left factoring is solution.

Comments

If left factoring is removed from the grammar then are two grammars equivalent?

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yes. But that grammer is left factored.

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So two grammars can be equivalent but not necessarily both be LL(1)?

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When two grammer generate same language they will be equivalent . example left recursive or right recursive.

Answer 2

Obviously given grammer suffers from common prefix probblem so it can't be LL(1) gammer.
LL is GMRAMMER not language so it will depend on grammer.

What you have done is you converted that grammer into other (obviously equivalent) grammer and then you are finding is it LL(1) or not. Whatever you have done that is correct for your newely generated grammer but not for original grammer.

So in the process of finding LL(1) Grammer dont  do anything with original grammer else answer will be different.

Answer 3

This grammar is not LL(1)

Explanation

S->ab    Will be kept under the first of S->ab which is 'a'

Similarly S->ac will be also kept under the first of S->ac which 'a'

So under same enteries how we can put more production.

So this grammar is not LL(1)

Answer 4

Not LL1