Hence: 
, proving the equivalence as defined.
Note that, to construct an equivalent Moore machine from a Mealy machine we cannot adopt the reverse process given in the above constructions i.e. simply push the output associated with a transition to the state (where this, transition leads to) to be considered as the output produced by the state. This is because, there may be two transitions going to a state with different outputs associated with it as shown below.
This is an ambiguous situation as we are not sure which output symbol (0 or 1) is to be associated with the state q |
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