See the above reply where I gave an example with both representations. Agreed, the machine representation is independent of the machine itself, it's the same m

See the above reply where I gave an example with both representations. Agreed, the machine representation is independent of the machine itself, it's the same mathematical object. So what I was talking about was how to represent using only a relation which describes the possible next states given the current one. This is the most common definition of a state machine, and for me, it's a cleaner representation since you avoid referring to each edge in the state graph explicitly.