I have some modified automata and the task is to give the type of Chomsky hierarchy to it. All task is between type 3 and 0 noninclusive. For regular languages there are lot of tools and I can check it without problems, Turing Machine equivalent is also easy task, and there will be no such examples.
Now the question: is it sufficient to show that automaton can accept specified language of given type? From what I checked it would be sufficient to show equivalence to for example to NPDA, so I assume that if machine handles language that at least NPDA accepts it would be sufficient.
For example if machine can accept $a^nb^n$, it is type 2. If machine can accept $a^nb^nc^nd^n$ it is type 1? If not are there better examples of such languages or what steps should I follow?