Can a DFA (Deterministic Finite State Machine) have 1 loop for multiple inputs

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A deterministic state machine example

For the DFA shown above, is it ok if you can put all those inputs from B into 1 loop?
eg. 1 loop going from B to B, with inputs 2,4,6,8.

And can I put the digits going out of A, into one line?
I say this to reduce clutter.

Or does each input need to be clearly defined like this?

And would the Non-deterministic version of this FSM look the same?

Best Answer

If I am understanding you correctly, you're completely right.

The DFA that you have shown could also be written as follows. However, if this is for a class, you might want to double check with your professor just in case. As an undergrad I had a professor who would not let us use common abbreviations like these, even though they are used "in the wild" with little to no confusion.

a simplified version of OP's DFA


I hope this helps ^_^

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