Question 4 (25 marks): The following transition system describes a process in which people switch on or off the light, and finally leave the room. We use four events, on, off, leave and error, to model the system, and please use the diagram to answer the questions.

Q4.a) Please give a trace which contains the event error, and explain the scenario or meaning of the trace.

Q4.b) Does the process P= on->P [ ] off->P satisfy the above transition system, or any trace of P is NOT included in the transition system. Please explain why it satisfies or does not satisfy.

Q4.c) We have the following parallel composition SYS which consists of P and Q with an interface. Please work out the behaviour of SYS, and prove whether it can satisfy the above transition system. P = error -> SKIP [ ] off -> leave -> SKIP Q = on-> SKIP ||| off -> leave -> SKIP SYS = P [| {error, off, leave} |] Q where [ ] denotes external choice, ||| for interleave and [|{error, off, leave}|] for interface parallel.

Q4.d) Please work out the FDR scripts for the above transition system.