EECS20N: Signals and Systems

Side-by-Side Composition

Consider two state machines connected in parallel:

The components are

StateMachineA = ( StatesA , InputsA , OutputsA, updateA, initialStateA)

StateMachineB = ( StatesB, InputsB, OutputsB, updateB, initialStateB )

Let the composition be given by

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

Definition of the composition:

  • States = StatesA ×StatesB
  • Inputs = InputsA × InputsB
  • Outputs = OutputsA × OutputsB
  • initialState = (initialStateA , initialStateB )
  • update((sA, sB), (xA, xB)) = ((s'A, s'B), (yA, yB))

where

(s'A, yA) = updateA(sA , xA)

(s'B, yB) = updateB(sB , xB)

Stuttering element:

  • stutter = (absent, absent)