Spring semester 2006 ESE601: Hybrid Systems Review material on discrete event systems I.

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Spring semester 2006

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

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

Printer data buffer

in

in

in

in

out

out

out

overflow

Data in

Data out

printer

A printer

out

printready

jamfix

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

7 7 7 7 7

1. Insert coin

2. Pull handle

3. Win if the combination is good, otherwise lose.

coinhand

le

handle

win

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

21

3

4

out

printready

jamfix

Execution of transition systems

Automata

Automata

21

3

4

out

printready

jamfix

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

1

2

1

2

3a b a

a

b

1,1 2,2 1,3a b

a

1,2 2,3a

a

2,1

a

Composition of automata

Composition of automata

Composition of automata

in

in

in

in

out

out

out

overflow

21

3

4

out

printready

jam

Composition and languages

Example

1

2

3 4

5

a

b

b

c

c

a

1

2

bc

d

1,1 2,1a

3,2b

5,1c

a

4,2

d

Only accessible states

Composition and languages

Input – output automata

Input – output automata

Input – output automata

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