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    Currently studying Finite-state automata, and I'm having some trouble understanding how the method to translate an FSA that uses epsilon into one that doesn't works.

    So let's say we have the automata shown below:

    The first step is easy enough: just creating a transition table for the automata.
    The second stage, adding the ε*, I understand too.
    The third stage is where I have a question. As the table for the third stage shows below:

    *If the image above is not viewable (forum refuses to show it for some reason) then refer to http://imgur.com/a/i2ZYo for the image.

    I'm unsure what the set inputs are meant to represent. So for instance the first input (left q0, top a) which, after taking 0 ε, q0 can take the input a. But does this input of {q0} represent where the FSA is after taking a? Or does it show just what it can take after taking ε?

    The example FSA doesn't make this clear, as after taking a, q0 will still be on q0, so I'm unsure if this means that the input on the table is where it ends up after taking the input or just what it is able to take.

    Thanks. All help appreciated!
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