1. Spring semester 2006 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 1.Insert coin(s) 2.Choose tea or coffee 3.Put the cup on the tray 4.Drink is ready coin tea coffee cup ready cup

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

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 77777 1.Insert coin 2.Pull handle 3.Win if the combination is good, otherwise lose. coin handle win 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. 21 3 4 out print ready jam fix

10. Execution of transition systems

11. Automata

12. 21 3 4 out print ready jam fix

13. Execution of automata

14. Regular languages

18. Regular expressions

19. Accessibility

20. Blocking property

21. Co-accessibility

23. Composition of automata

24. 1 2 1 2 3 a b a a b 1,12,21,3 ab a 1,22,3 a a 2,1 a

25. Composition of automata

27. in out overflow 21 3 4 out print ready jam

28. Composition and languages

29. Example 1 2 34 5 a b b c c a 1 2 bc d 1,12,1 a 3,2 b 5,1 c a 4,2 d Only accessible states

30. Composition and languages

31. Input – output automata