# Does $LL(K)$ grammar has one to one correspondence with $DCFL$? [duplicate]

• 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 ?