And one more doubt i am facing for so many days ---- LR(0) generate the DCFL with prefix property (DPDA with empty stack). (Line said by Arjun sir in discussion part )please give me some references so that I can clear this doubt i couldn't understand that what is dpda with empty stack

we can make only one parse tree for every string generated by this grammar , moreover the language generated by this grammar is set of all the even length palindrome

so it is unambiguous

now it is not LL(1)

because S ⇒ aSa | bSb |ε

here the follow of S is a,b ,$ that is match with the first of right hand side

it means is row S and column a contain 2 entry and same thing will happen for column b watch the diagram

a

b

$

S

S->aSa,S->epsilon

S->bSb,S->epsilon

S->epsilon

now the given grammar is not DCFL so it is not LR(k)

1. Each DCFL can be generated by a corresponding LR(k) grammar and each LR(k) grammar generates one DCFL (one-to-one correspondence).
2. no DCFL is inherently ambiguous.
3. Each LR(k) grammar is unambiguous grammar, but each unambiguous grammar need not to be LR(k). .
5. An inherently ambiguous language can only be non-deterministic while an non-deterministic language may or may not be inherently ambiguous.

more about DCFL

1) there are some DCFLs which does not have an LL(k) grammar (see ref below).

2) and for any DCFL, we can always have an LR(K) grammar