I have the following excercise:
Demostrate this grammar is ambiguous:
S-> bA | aB
A-> a | aS | bAA
B-> b | bS | aBB
By the theory that I've read a grammar can be ambiguous if:
1) A string W ∈ L(G), generates two differents trees
2) Makes 2 or more left/right derivations
So, i couldnt determinate a string that confirms 1) , so i've
tryed with 2).For what i understand just need 2 reflexive derivations to get my grammar as ambiguous??
for example:
w=bbaa S->bA->bbAA->bbaA->bbaa
^^--here i made two reflexive/recursive derivation
Is this correct as i described or need more detailled information ?
PD: is there any tip for get strings that generates two threes ??
No, this is not a correct demonstration of ambiguity.
Your understanding of point #2 is flawed. A grammar G is ambiguous iff some w in L(G) has more than one leftmost (or rightmost) derivation. You've shown one leftmost derivation for w=bbaa, so if you could show another (i.e., a different leftmost derivation for the same string), that would demonstrate ambiguity. However, there doesn't appear to be one, so you'll have to pick a different string.
Note that this has nothing to do with whether a derivation involves the application of recursive/reflexive productions.