Spring semester 2006 ESE601: Hybrid Systems Review material on discrete event systems I
Spring semester 2006 ESE601: Hybrid Systems Review material on discrete event systems I.
Dec 22, 2015
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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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