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Which of the following statements is FALSE?

1. Any DCFL has an equivalent grammar that can be parsed by a SLR(1) parser with end string delimiter
2. Languages of grammars parsed by LR(2) parsers is a strict super set of the languages of grammars parsed by LR(1) parsers
3. Languages of grammars parsed by LL(2) parsers is a strict super set of the languages of grammars parsed by LL(1) parsers
4. There is no DCFL which is not having a grammar that can be parsed by a LR(1) parser

### 13 Comments

d false
Which is that DCFL?

@Arjun Sir, is the answer C?

my reasoning is as follows,

consider a grammar

S -> aA/aB

A -> cA/c

B -> bB/b

The above grammar is LL(2).

now the above grammar can be converted into LL(1) as follows

S -> aS'

S' -> cA/ϵ

S' -> bB/ϵ

similarly every other LL(2) grammar should be convertable to LL(1) grammar.

No, that is wrong. For every $k$ Language of LL(k) is a strict subset of Language of LL(k+1)

@Arjun Sir, Option A holds for both SLR(1) and LR(0) then?

Yes. It does.
$B?$

as, $Lang(LR(2))=Lang(LR(1))$
Yes.
reshown

Option A holds for both SLR(1) and LR(0) then?

https://gatecse.in/category/compiler-design/

Sir, here it is mentioned that

Language of LR(0) (set of all LR(0) grammars) is same as "DCFL having prefix property"

Then how can Option A hold true for LR(0)?

Yes. It does. SLR parser uses LR(0) items only.

Reffering from the diagram in... https://gateoverflow.in/1470/gate1999-1-17#16773

Iam confused how B is false.  @Arjun sir please help. which one of them is true.

edited by

@suraj20041995 diagram is referring to parsers…..In question languages of grammar is mentioned….

important points

dcfl ?

## 3 Answers

B is false because LR(k) is equivalent to LR(k+1) grammar not any superset relationship
Answer is B

LR(0) ⊂ LR(1) = LR(2) ........LR(k) = LR(k+1)  ; for k >= 1 : LR(k)=LR(k+1)

so, Languages of grammars parsed by LR(2) parsers is not a strict super set of the languages of grammars parsed by LR(1) parsers

although they both are same ;

if you compare their grammars :

LR(0) ⊂ LR(1) ⊂ LR(2) ........LR(k) ⊂ LR(k+1)

### 2 Comments

Why you have mentioned LR(2) as a superset of LR(1)
edited

1 . LR(2) Grammar is super-set of LR(1) grammar .

2 . Languages of grammars parsed by LR(2) parsers is same as Languages of grammars parsed by LR(1) parsers

please make sure , 1 statement is talking about grammar , 2 is talking about Language

A,C,D are correct options. B is false.
Answer:

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