There a 3 types of FSMs a Mealy Machine, a Moore Machine and a Finite State Automata.
A Finite State Automata (FSA) is a FSM which has a finishing state and only outputs a YES/NO answer based on which state the input string ends on.
A Mealy Machine is a FSM where the output is on the transistions opposed to the states.
A Moore Machine is a FSM where the output is on the states opposed to the transisitons.
A FSM/FSA can be represented in a variety of ways the most common is a State transition Diagram.
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| This is an example of a FSA as shown by a State Transition Diagram. The arrow with no number above it shows the Starting State. And the yellow circle around State 2 indicates that it's the state which will give an output of YES. |
Current State: S1 S1 S2 S2 S3 S3
Input: 0 1 0 1 0 1
Next State: S2 S3 S3 S3 S1 S1
Output: A B C B C B
This table shows that in State 1 if you input 0 the FSM would be A and the next State would be Sate 2.
The third way to represent a FSM is as a Transition Function. These have the standard formula of (Input Symbol, Current State) -> (Output Symbol, Next State). For example (1, S3) -> (A, S2) would mean that if you are currently in State 3 and if you input 1 the FSM will output A and move to State 2.
Finally there are 2 types of FSM/FSA, Deterministic and Non-Deterministic. Deterministic means there is only 1 transition for each input while Non-Deterministic means there's more than one possible transition per input allowing for more than 1 route round a State Transition Diagram.
Oh and also a Halting State is a state with no outputs.
