Sets and Functions View

A state machine is a 5-tuple

StateMachine = (States, Inputs, Outputs, update, initialState)

These five elements define a system with input signals

InputSignals = [Naturals₀ ® Inputs]

and output signals

OutputSignals = [Naturals₀ ® Outputs]

The input alphabet Inputs and output alphabet Outputs define the symbols of the input and output event sequences. The remaining three elements define the mapping from input to output signals.

• States is the state space (a set)
• initialState is the initial state (a member of States)
• update is the update function.

The update function has the form

update: States ´ Inputs ® States ´ Outputs