Is every language that is generated by a NDCFG (Non Deterministic Context Free Grammar) , CSG (Context Sensitive Grammar) and Unrestricted Grammar inherently ambiguous ?
I think so because they dont have a DPDA accepting that language. And as far as I understand if a language is not inherently ambiguous, it must have a DPDA accepting it.
So, if that is true, then the language {anbn, n>=0} U {anb2n, n>=0} is inherently ambiguous, because there is no DPDA accepting that language. But if I see the grammar for the language:
S -> A | B
A -> aAb | ε
B -> aBbb | ε
and I consider the string "aabb", I dont get two parse trees (which is a necessity for a grammar to be ambiguous ! And a language can be "inherently ambiguous" only if it has NO UNAMBIGUOUS GRAMMAR REPRESENTATION.
But here we get an unambiguous grammar for a language that is not accepted by DPDA. So my question is : is this language inherently ambiguous?
Also in case of CSL and REC, there are no "parse trees" as such. So how do I determine if the language is inherently ambiguous or not?