Hybrid Embedded Timed Automata Analysis 2004

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EECE 396-1

Hybrid and Embedded Systems: Computation

T. John Koo, Ph.D.

Institute for Software Integrated Systems

Department of Electrical Engineering and Computer Science

Vanderbilt University

300 Featheringil l Hall April 6-15, 2004

[email protected]

http://www.vuse.vanderbilt.edu/~kootj

mailto:[email protected]

mailto:[email protected]



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Analysis: Timed Automata



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Topics Bisimular Transition Systems

Transition Systems

Forward and Backward Reachability Algorithms

Simulation and Bisimulation Relations

Transition Systems and Quotient Transition Systems

Bisimulation between Transition Systems

Bisimulation Algorithm

Bisimulations of Timed Automata

Executions of Timed Automata

Region Equivalent Relation and Parti tion

Ref:

[1] R. Alur, T.A. Henzinger, and P.-H. Ho. Automatic Symbolic Verificationof Embedded Systems. IEEE Transactions on Software Engineering22:181-201, 1996.

[2] J. Lygeros, Lecture Notes on Hybrid Systems, Cambridge, 2003. [3] J. Lygeros, C. Tomlin, and S. Sastry, The Art of Hybrid Systems, July

2001.

http://www-cad.eecs.berkeley.edu/~tah/HyTech///www.eecs.berkeley.edu/~tah/Publications/automatic_symbolic_verification_of_embedded_systems.html









Analysis: Timed AutomataBisimular Transition Systems



Transition System



Forward and Backward

Reachability Algorithms



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Simulation and Bisimulation

Relations



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Relations



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Relations



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Relations



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Relations



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Relations



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Relations



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Relations



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Relations



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Relations



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How?



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Analysis: Timed AutomataBisimulations of Timed Automata



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Timed Automata



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Timed Automata



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Timed Automata



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Timed Automata



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Timed Automata



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Timed Automata



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Timed Automata



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Timed Automata



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Timed Automata



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Timed Automata



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Hybrid Automaton



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Hybrid Automaton

i

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tfinite

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tinfinite



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Hybrid Automaton

i

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tfinite

i

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tZeno



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Hybrid Automaton Blocking

No Infinite executions for some initial states

Source of blocking

Cannot continue in domain due to reaching the boundary of the

domain where no guard is defined

Have no place to make discrete transit ion to

Definition: A hybrid automaton H is non-blocking if for every

initial condition there exists at least one infinite execution

?



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Hybrid Automaton Zeno Executions

Infinite execution defined over finite time

Infinite number of transitions in finite time

Transition t imes converge

Definition: A hybrid automaton H is zeno if there exists an

initial condition for which all infinite executions are Zeno



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Transition System



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Region Equivalence Relation

R i E i l R l ti



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Ti d A t t



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Timed Automata

Ti d A t t



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Timed Automata



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eg o qu a e ce e at o




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g q



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Hybrid Embedded Timed Automata Analysis 2004

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