# What are non-isomorphic NFAs

I came across the following problem while doing my Formal Language class assignment and hope someone can give me some hints:

1. I have $$\Sigma = \{0,1\}$$ and $$L=\{x0a \mid x \in \Sigma^*, a \in \Sigma\}$$, namely $$L$$ contains all strings whose second-to-last character must be a $$0$$.
2. I have found that there are four equivalence classes of $$I_L$$, namely $$[\epsilon], , , $$, and I'm able to construct a DFA using this four equivalence classes to accept the language $$L$$.
3. Then, I'm asked to show that there are at least three non-isomorphic NFAs of minimum size that all can accept $$L$$. I think the smallest NFA must have at least three states since if a NFA has only two states, this implies that there exists a single character that can be accepted by this NFA which is not true for the language we have.

Can someone provide some hints regarding how to approach this?

Once we know this we can play with the automaton. Create three states: initial state $$0$$, seen letter $$0$$ as state $$1$$, and accept after $$0a$$ as state $$2$$. From this we can add extra edges to ensure that all and only strings ending in $$0$$ will reach the middle state $$1$$. 