EECS20N: Signals and Systems

Feedback Composition

Consider two state machines connected with a feedback loop:

Assumption:

  • OutputsA ⊂ InputsB
  • OutputsB2 ⊂ InputsA2

Definition of the composition:

  • States = StatesA × StatesB
  • Inputs = InputsA1
  • Outputs = OutputsB1

updates function is found by iteration to a fixed point:

  • Start with unknown on the feedback arc
  • Foreach state machine:
    • If output can be determined, produce it
    • If state transition can be determined, take it
  • Repeat until no progress is made.

Two possible outcomes:

  • All outputs are determined
  • Some signals are still unknown

In the latter case, the composition is ill formed.