how can i prove that this grammar is ambiguous?

问题

S -> bA|aB
A -> a|aS|bAA
B -> b|bS|aBB

Any easy method other than trying to find a string that would generate two parse trees ?

Can someone please give me a string that can prove this.

回答1:

There is no easy method for proving a context-free grammar ambiguous -- in fact, the question is undecidable, by reduction to the Post correspondence problem.

回答2:

There is a string though: bbaaba

S -> bA -> bbAA -> bbaA -> bbaaS -> bbaabA -> bbaaba
S -> bA -> bbAA -> bbaSA -> bbaaBA -> bbaabA -> bbaaba

来源：https://stackoverflow.com/questions/4878418/how-can-i-prove-that-this-grammar-is-ambiguous