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

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)

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

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

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.

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

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.

Transition systems

Transition systems 4 jam out fix 1 2 print 3 ready

Execution of transition systems

Automata

Automata 4 jam out fix 1 2 print 3 ready

Execution of automata

Regular languages

Regular languages

Regular languages

Regular languages

Regular expressions

Accessibility

Blocking property

Co-accessibility

Co-accessibility

Composition of automata

Composition of automata b 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

Composition of automata

Composition of automata

Composition of automata in out 4 jam in out out 1 2 print in out 3 ready in overflow

Composition and languages

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

Composition and languages

Input – output automata

Input – output automata

Input – output automata