1. Review material on discrete event systems I
ESE601: Hybrid Systems
Review material on discrete event systems I

2. Contents Examples (5) Transition systems and automata (6)
Languages and regular expression (6)
Reachability and blocking property (5)
Composition of automata (5)
I/O automata (5)

3. A vending machine Insert coin(s) Choose tea or coffee
Put the cup on the tray
Drink is ready
ready
cup
tea
coin
coffee
cup

4. Printer data buffer Data in in out in out in out printer Data out in
overflow

5. A printer
out
print
ready
jam
fix
The printer receives data from the buffer, and print it out. Once the printout is ready, the printer is ready to receive new data. While printing, the paper can jam and need to be fixed before the printing process can resume.

6. A slot machine Insert coin Pull handle
Win if the combination is good, otherwise lose. 7 7 7 7 7
win
handle
coin
handle
lose

7. Modeling recap Events are time-abstract.
Just like modeling of continuous systems, the level of detail is ‘modeler dependent’.
Events are not necessarily equipped with any notion of ‘internal-external’ or ‘input-output’.
Compositionality is possible (to be discussed later).
There can be non-determinism.

8. Transition systems

9. Transition systems 4
jam
out
fix 1 2
print 3
ready

10. Execution of transition systems

11. Automata

12. Automata 4
jam
out
fix 1 2
print 3
ready

13. Execution of automata

14. Regular languages

15. Regular languages

16. Regular languages

17. Regular languages

18. Regular expressions

19. Accessibility

20. Blocking property

21. Co-accessibility

22. Co-accessibility

23. Composition of automata

24. Composition of automatab
1,1
2,2
1,3 1 1 a a a b a a a 3 a
1,2
2,3
2,1 2 2 b

25. Composition of automata

26. Composition of automata

27. Composition of automatain
out 4
jam in
out
out 1 2
print in
out 3
ready in
overflow

28. Composition and languages

29. Example 1 a 1 2 c a c b b d 3 4 2 c Only accessible states b 1,1 2,1 a
3,2 b
5,1 c
4,2 d 5

30. Composition and languages

31. Input – output automata

32. Input – output automata

33. Input – output automata