I have received a question about how to approach DFSM minimization in one of the previous posts. This is an attempt to answer that question.

## What is DFSM minimization?

First, let us consider what does it mean for two DFSM to be **equivalent**? Imagine having two DFSM that both accept the same input symbols. You then pass all the possible inputs to those two machines. If and only if the answers are the same for all the inputs then the two machines are equivalent. That is: they accept exactly the same inputs, even though their inner workings might not be the same.

This means that there are many equivalent DFSM. For example all three DFSM in the below picture accept the same input which can be written as a regular expression (0+1)^{*}.

The three DFSM vary in the number of states and also in the number of the transitions. Nonetheless, I hope you will agree with me that they all accept the same input.

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