The following is a sequence of configurations leading to the acceptance of the string [ [ ] [ ] ] [ ].
Equivalence of acceptance by final state and empty stack.
It turns out that the two definitions of acceptance of a language by a PDA - accpetance by final state and empty stack- are equivalent in the sense that if a language can be accepted by empty stack by some PDA, it can also be accepted by final state by some other PDA and vice versa. Hence it doesn't matter which one we use, since each kind of machine can simulate the other.Given any arbitrary PDA M that accpets the language L by final state or empty stack, we can always construct an equivalent PDA M with a single final state that accpets exactly the same language L. The construction process of M' from M and the proof of equivalence of M & M' are given below.