EECS20N: Signals and Systems

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