Stuttering removal-developing mealy and moore style implementations of an interactive component

An interactive system operates by an ongoing communication between its components which send and receive messages on their input and output channels. Stream functions describe the component's input/output behaviour mapping input streams to output streams. State transition machines describe the component's state-based implementation. We adapt classical Mealy machines and classical Moore machines as needed for the state-based modelling of interactive components. As our main contribution, we compare the formal methods how to implement a stream function by a Mealy resp. a Moore style state transition machine in a correctness preserving way. Both transformations involve history abstractions which relate observable input streams with internal states. We compare the different implementation frameworks by constructing a Mealy style and a Moore style implementation for the same component. We illustrate the approach with a component which removes subsequent duplicate messages in an input stream which arose through stuttering.