Cascade Composition

Consider two state machines connected in series:

The components are

StateMachine_A = (States_A , Inputs_A , Outputs_A , update_A , initialState_A )

StateMachine_B = (States_B , Inputs_B , Outputs_B , update_B , initialState_B )

Let the composition be given by

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

Assumption:

Definition of the composition:

where

(s'_A, y_A) = update_A (s_A, x)

(s'_B, y_B )= update_B (s_B, y_A)

Stuttering element: