Exercise 1. Modeling#
Model the operations in a swimming pool using an automaton
A swimming pool comprises 𝑐 cabins to change and 𝑝 baskets to deposit clothes.
A user can enter the pool only if a cabin is free.
Once he has a cabin, he has to wait for a basket to change and deposit his clothes.
Then it releases the cabin and enter the swimming pool.
He can leave only if a cabin is free.
After changing, he frees the cabin and basket.
Finally, he leaves the pool.
Question 1#
Model the operations in a swimming pool, using an automaton, in the case where there is only one basket. You can use the actions described in the table below.
| A user can enter the pool only if a cabin is free. | TC: Take Cabin |
| Once he has a cabin, he has to wait for a basket to change and deposit his clothes. | TB: Take Basket |
| Then it releases the cabin and enter the swimming pool. | ES: Enter Basin |
| He can leave only if a cabin is free. | LS: Leave Basin |
| After changing, he frees the cabin and basket. | LB: Leave Basket |
| Finally, he leaves the pool. | EXIT: exit pool |
Question 2#
Model the swimming pool with 1 cabin and 2 baskets.
Question 3#
Try with \(𝑐=2\) cabins and \(𝑝=2\) baskets. (Do not make it completely.) Would you model the system with 5 cabins and 8 baskets?
Exercise 2. SCC#
Compute the DFS order and the SCC for the following graph.
| # | id | lw |
|---|---|---|
| 0 | a | 0 |
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 |
Exercise 3. Synthesis#
Find an example of system (a graph) with two actions, 𝑎 and 𝑏, where 𝑎 is quasi live and 𝑏 is live