I commented on your step function in another comment so I'm going to skip that.
Your DFA construction, while a bit incomplete (you don't say how you do the transitions), achieves roughly the same thing as Levenshtein automata do. But you spend significantly more time to construct it. The point of the original paper was not to show that DFAs can be used to compute Levenshtein distance, but to show how to do it quickly and efficiently.
Comments
I commented on your step function in another comment so I'm going to skip that.
Your DFA construction, while a bit incomplete (you don't say how you do the transitions), achieves roughly the same thing as Levenshtein automata do. But you spend significantly more time to construct it. The point of the original paper was not to show that DFAs can be used to compute Levenshtein distance, but to show how to do it quickly and efficiently.
I replied to this in the other thread to avoid splitting the conversation in two.