- Does $LL(K)$ grammar has one to one correspondence with $DCFL$ ?
If I am understanding right, then the given statement says that $2$ distinct $LL(k)$ have one to one mapping, i.e they should not generate the same $DCFL$.
Let us say:-
$G1 : S-> aB,B->a$ generates $aa$ and $G2: S->aa$ also generates $aa$.
Here, both the grammars are $LL(1)$, and generate the same language $aa$ implying many to one mapping and not one to one .
Moreover, If we take a $DCFL$, $$a^n\bigcup a^nb^n$$, it has no $LL(k)$ grammar for it and another $DCFL$, say $$a^m b^{m+n}$$, then it also has no $LL(K)$ grammar for it.
- Similarly, I think the statement that "Does $LR(K)$ grammar has one to one correspondence with DCFL" is also false.
Am I right in the reasoning of both the above statements ?
If both are false, then what should be the correct interpretation of the above statements ?
