A Finite State Machine is defined using the following properties:

- S (finite set of states)
- s₁ (initial state)
- δ (state transfer function)
- λ (output function)
- X (finite input alphabet)
- Y (finite output alphabet)

FSMs can be represented graphically using a basic statechart notation.

A "deterministic" FSM is one where there os only one possible transition for each state with a given input. All FSMs are considered to be deterministic.

An "initially connected" FSM is one in which all nodes can be reached from the initial node / state. All FSMs should be initially connected. An FSM is "strongly connected" if any two nodes in the FSM can be connected through a sequence of transitions.

If two states are non-distinguishable, they are "equivalent". This means that one of them can be removed as they do not both need to exist. An FSM is "minimal" if it contains no equivalent states.

A Reset operation will take an FSM back to its initial state. In the case of a real system, this reset operation may be an on/off switch.

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