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Week 5

• Synchrony
• Side-by-side
• Cascade
• Example
• Product-form
• Answering machine
• Series-Parallel
• Playback
• Composition
• Steps
• Feedback
• Example 1
• Example 2
• Example 3
• Example 4
• Delay

Consider a set of interconnected components, where each component is a state machine, as in:

We construct a state machine model for the composition that is synchronous and reactive:

• The reaction of the composite consists of exactly one reaction of each component.
• The reaction of the composite is triggered by an input to the composite.
• The component reactions are simultaneous and instantaneous.
• The output of each component is simultaneous with its input.
• The output of the composite is simultaneous with the input to the composite.
• The output of each component is visible to its destination in the same reaction.

Such machines react at a rate determined by the environment in which they operate. We have to be particularly careful with feedback compositions. Synchronous/reactive models are used in practice in

• circuit design, where they are used extensively, and
• software design, where they are used in specialized languages for embedded system design.