Bisimulation as congruence in the behavioral setting

1
Bisimulation as congruence in the behavioral
setting

• Agung Julius
• Dept. Electrical Systems Engineering
• University of Pennsylvania
• with Arjan van der Schaft (University of
  Groningen)

CDC/ECC 2005, Seville, Spain.
2
Talk Layout

• Motivational background
• States in the behavioral setting
• Bisimulation
• Bisimulation as congruence
• Concluding remarks

3
Motivation
analyze
4
Abstraction of complex systems
analyze
analyze
5
Congruence
6
Talk Layout

• Motivational background
• States in the behavioral setting
• Bisimulation
• Bisimulation as congruence
• Concluding remarks

7
Behavioral systems theory
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Dynamic maps and state maps
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Concatenation
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State maps
11
Talk Layout

• Motivational background
• State systems in the behavioral setting
• Bisimulation
• Bisimulation as congruence
• Concluding remarks

12
Bisimulation in concurrent systems
b
b
a
a
b
a
b
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Bisimulation of state systems
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Bisimulation of state systems
15
Talk Layout

• Motivational background
• State systems in the behavioral setting
• Bisimulation
• Bisimulation as congruence
• Concluding remarks

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Composition of state systems
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Bisimulation as congruence
(S ,x )
(S ,x )
1
1
2
2
18
Talk Layout

• Motivational background
• State systems in the behavioral setting
• Bisimulation
• Bisimulation as congruence
• Concluding remarks

19
Concluding remarks
Thank you for your attention!!