ACE Grand Test 2 ( Compiler Design)

Question

Consider the grammar :

$S\rightarrow SS+ | SS* | a$

Which of the following is true:

A) SLR(1) but not LL(1)

B) LALR(1) but not  SLR(1)

C) LR(1) but not LALR(1)

D) Neither LL(1) nor LR(1)

I feel the grammar is unambiguous as I couldn't get more than one parse tree for any inputs I tried. (Their key is suggesting the answer D saying it's ambiguous)
Shouldn't A be the answer? Please guide me and correct me if I'm wrong

Comments

https://gateoverflow.in/150318/ace-gate-test-series-2018 

---

.

• GIVEN GRAMMAR IS LEFT RECURCIVE .If a grammar is left recurcive then it never be LL(1). 

• It is LR(0) HENCE SLR also.so option a is true.

• 

   

Answer 1

I think it is SLR(1) becoz of no R/R or S/R conflict but not LR(1) or LL(1)

therefore ans should be A

Comments

If It is SLR Then it must be a LR(1) TOO .

---

$LR(0) \subseteq SLR(1) \subseteq LALR(1) \subseteq LR(1)$

So if it is LR(0) then definitely it 

will be SLR(1), LALR(1) and also LR(1)

See this ->

The containment rules are the following:

• Every LR(0) grammar is also SLR(1), but not all SLR(1) grammars are LR(0).
• Every SLR(1) grammar is also LALR(1), but not all LALR(1) grammars are SLR(1).
• Every LALR(1) grammar is also LR(1), but not all LR(1) grammars are LALR(1).
• Every LL(1) grammar is also LR(1), but not all LR(1) grammars are LL(1).
• Every LL(0) grammar is also LR(0), SLR(1), LALR(1), LR(1), and LL(1).