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Questions about mathematical devices that read an input stream symbol by symbol and use a state transition map to produce an output stream, maybe using secondary storage.
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Why are these states equivalent on this translation table
When you say equivalent you need to keep in mind to look if there is no word in length k that separates them.
Moreover you you can see that for a word in length 1 :
$If w_1 = 1 $ then F and G
ente …