EECS20N: Signals and Systems

Cascade Composition

Consider two state machines connected in series:

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 )

Assumption:

  • OutputsA ⊂  InputsB
Definition of the composition:
  • States = StatesA × StatesB
  • Inputs = InputsA
  • Outputs = OutputsB
  • initialState = (initialStateA , initialStateB )
  • update((sA , sB), x) = ((s'A , s'B), yB)

where

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

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

Stuttering element:

  • stutter = absent