Compiler Design(gATE 2010)

Question

GATE 2010 Question

The grammar S→aSa∣bS∣c is 

1. LL(1) but not LR(1)
2. LR(1) but not LL(1)
3. Both LL(1) and LR(1)
4. Neither LL(1) nor LR(1)

I have 2 small doubt

First Doubt:-If a grammer is LL(1) then it is always LR(0) ? Is there any grammer which is LL(1)  and cannot be parsed by LR(0) ?

Second doubt :- Can any one tell me the above question is write or wrong because they have given LR(1) parser and i haven't heard about LR(1).I have heard about  Brute force ,recursive descent,operator presedence,LL(1) LR(0) SLR(1) LALR(1) CLR(1).So what is the difference between LR(0) AND LR(1) and which one is more powerfull ?

Comments

Thanks :)

Answer 1

First Doubt : A grammar parsed by LL(1) must also be parsed by LR(1) Parser but may not by LR(0)

For e.g 

S. ---> AaAb 

S ---> BbBa

A ---> €

B ---> €

Second doubt : LR(1) also known as canonical LR(1)

So LR(1) and CLR(1) same.

Comments

thanks:)

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@Himanshu LL(1) is subset of LR(1)

Also LR(1) are DCFL.

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In diagram where will be LL(0)??

Answer 2

CLR(1) is also called as LR(1)

Comments

Thanks

Answer 3

1. please check this i am correct or not