Real Real Real Time Real-Time Time Time Model Checking Model Model Checking Model Checking Checking Patricia Bouyer-Decitre Patricia Bouyer-Decitre Kim Kim G Larsen Kim Kim G. . Larsen Larsen Larsen Nicolas Markey Nicolas Markey
Timed Timed Automata Timed Timed Automata Automata Automata .. .. and Prices Prices and Games Games Patricia Bouyer-Decitre Patricia Bouyer-Decitre Kim Kim G Larsen Kim Kim G. . Larsen Larsen Larsen Nicolas Markey Nicolas Markey
Model Checking Model Checking Time Cost Probability No! System Description Debugging Information Debugging Information TOOL Yes Yes Prototypes Requirement A ( req ⇒ A ♦ grant) Executable Code Test sequences A ( req ⇒ A ♦ t<30s grant) A ( req ⇒ A ♦ t<30s,c<5$ grant) A ( req ⇒ A ♦ t<30s , p>0.90 grant) A ( A ♦ t) QM QMC, PhD PhD School School, Ma , March 3, 3, 201 2010 Kim Larsen [3] Kim Lars en [3]
Synthesis Synthesis ? Time Cost Probability No! System Description Debugging Information Debugging Information TOOL Yes Yes Control Strategy Requirement A ( req ⇒ A ♦ grant) A ( req ⇒ A ♦ t<30s grant) A ( req ⇒ A ♦ t<30s,c<5$ grant) A ( req ⇒ A ♦ t<30s , p>0.90 grant) A ( A ♦ t) QM QMC, PhD PhD School School, Ma , March 3, 3, 201 2010 Kim Lars Kim Larsen [4] en [4]
Overview Overview Introduction Introduction to Timed Automata Timed Automata Decidability Decidability and undecidability results undecidability results CLASSI C CLASSI C CLASSI C CLASSI C CLASSI C CLASSI C CLASSI C CLASSI C Timed Temporal Logics Temporal Logics CORA CORA CORA CORA UPPAAL UPPAAL UPPAAL .. (hands-on) UPPAAL (hands on) TI GA TI GA TI GA TI GA Timed Games Games Price P i P i ced Timed Automata d Ti d A t t TRON TRON TRON TRON Open Open Problems Problems PRO PRO QM QMC, PhD PhD Sch School, March March 3, 3, 2010 2010 Kim Lars Kim Larsen [5] en [5]
Timed Automata Timed Automata
UPPAAL (contributors) UPPAAL (contributors) @ AALborg AALborg @UPPsala @UPPsala Kim G Larsen Wang Yi Gerd Behrman Paul Pettersson Paul Pettersson Arne Skou John Håkansson Brian Nielsen Anders Hessel Alexandre David Pavel Krcal Jacob I Rasmussen Jacob I. Rasmussen Leonid Mokrushin Marius Mikucionis Shi Xiaochun Thomas Chatain @Elsewhere Emmanuel Fleury, Didier Lime, Johan Bengtsson, Fredrik Larsson, Kåre J Kristoffersen, Tobias Amnell, Thomas Hune, Oliver Möller, Elena Fersman, Carsten Weise, David Griffioen, Ansgar Fehnker, Jan Tretmans, Frits C W i D id G iffi A F h k J T F i Vandraager, Theo Ruys, Pedro D’Argenio, J-P Katoen,, Judi Romijn, Ed Brinksma, Martijn Hendriks, Klaus Havelund, Franck Cassez, Magnus Lindahl, Francois Laroussinie, Patricia Bouyer, Augusto Burgueno, H. Bowmann, D. Latella, M. Massink, G. Faconti, Kristina Lundqvist, Lars B D L t ll M M i k G F ti K i ti L d i t L Asplund, Justin Pearson..... QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Lars Kim Larsen [7] en [7]
Real Time Systems Real Time Systems sensors actuators Controller Program Plant Discrete Continuous Eg.: Realtime Protocols Pump Control Real Time System Air Bags A system where correctness not only A system where correctness not only Robots depends on the logical order of events Cruise Control but also on their timing!! ABS CD Players CD Players Production Lines QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Lars Kim Larsen [8] en [8]
A Dumb A Dumb Light Controller Light Controller QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Lars Kim Larsen [9] en [9]
Timed Timed Automata utomata [ Alur & Dill’89] Synchronizing action Reset Clock Guard Conjunctions of x~n n x: real-valued clock ADD a clock ADD a clock x QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [10] Kim Larsen [10]
A Timed A Timed Automata utomata (Semantics) States: Transitions: ( location , x= v) where v ∈ R ( Off , x= 0 ) ( Off x= 4 32 ) ( Off , x= 4.32 ) delay 4 32 delay 4.32 ( Light , x= 0 ) press? ( Light , x= 2.51 ) delay 2.51 ( Bright , x= 2.51 ) press? QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [11] Kim Larsen [11]
Intelligent Intelligent Light Controller Light Controller Invariant (Henzinger) QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [12] Kim Larsen [12]
Intelligent Intelligent Light Controller Light Controller X Note: Transitions: ( Light , x= 0 ) delay 103 ( Off , x= 0 ) ( Off , x= 4.32 ) delay 4.32 ( Light , x= 0 ) ( Li ht press? ? 0 ) ( Light , x= 4.51 ) delay 4.51 ( Light , x= 0 ) press? Invariants ( Light , x= 100) delay 100 ensures ( Off , x= 0) progress QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [13] Kim Larsen [13]
Timed Timed Automata utomata (formally) QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [14] Kim Larsen [14]
Timed Timed Automata utomata (formally) QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [15] Kim Larsen [15]
Timed Timed Automata utomata (formally) QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [16] Kim Larsen [16]
Timed Timed Automata utomata (formally) QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [17] Kim Larsen [17]
Example Example a b c QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [18] Kim Larsen [18]
x Kim Larsen [19] Kim Larsen [19] y b QMC, PhD School, March 3, 2010 2010 c QMC, PhD School, March 3, Example Example a
x Kim Larsen [20] Kim Larsen [20] y b QMC, PhD School, March 3, 2010 2010 c QMC, PhD School, March 3, Example Example a
x Kim Larsen [21] Kim Larsen [21] a a y b QMC, PhD School, March 3, 2010 2010 c QMC, PhD School, March 3, Example Example a
x a a Kim Larsen [22] Kim Larsen [22] a a y b QMC, PhD School, March 3, 2010 2010 c QMC, PhD School, March 3, Example Example a
Light Control I nterface f t l I t Li ht C
Light Control I nterface press? d release? touch! 0.5 ≤ d ≤ 1 press? 1 starthold! press? d release? endhold! d >1 gi knolog Interface touch! touch! touch! touch! onstek press? press? Control starthold! starthold! Program rmatio release? release? endhold! endhold! Light Light Infor User press? 0.2 release? … press? 0.7 release? … press? 1.0 2.4 release? … touch! starthold! endhold! Ø QMC, PhD School, March 3, 2010 24
25 Program Control Light Control I nterface starthold! starthold! endhold! endhold! h! h! touch! touch! QMC, PhD School, March 3, 2010 t t release? release? press? press? User gi knolog onstek rmatio Infor
26 Program Control starthold! starthold! endhold! endhold! touch! h! h! touch! QMC, PhD School, March 3, 2010 Light Control Netw ork t t release? release? press? press? gi knolog onstek rmatio Infor
Task Graph Scheduling
Resources Resources & Tasks Tasks & Composition Task Resource Synchronization Shared variable Sem antics: ( Idle , Init , B= 0, x= 0) ( Idle Init B 0 0) d(3.1415) ( Idle , Init , B= 0 , x= 3.1415 ) ( InUse , Using , B= 6, x= 0 ) use d(6) ( InUse , Using , B= 6, x= 6 ) done ( Idle , Done , B= 6 , x= 6 ) QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [28] Kim Larsen [28]
Task Graph Scheduling – Task Graph Scheduling – Example Example Compute : B C D (D * ( C * ( A + B )) + (( A + B ) + ( C * D )) 1 2 A * + + using 2 processors using 2 processors P2 (slow) P1 (fast) 4 3 * * + + C C + + 2ps 5ps * * 3ps 7ps 5 5 6 6 * * + D 5 10 15 20 25 P1 P1 2 2 3 3 5 5 6 6 P2 1 4 time QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [29] Kim Larsen [29]
Task Graph Scheduling – Task Graph Scheduling – Example Example Compute : B C D (D * ( C * ( A + B )) + (( A + B ) + ( C * D )) 1 2 A * + + using 2 processors using 2 processors P2 (slow) P1 (fast) 4 3 * * + + C C + + 2ps 5ps * * 3ps 7ps 5 5 6 6 * * + D 5 10 15 20 25 P1 P1 5 5 4 4 6 6 1 1 3 3 P2 2 time QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Larsen [30] Kim Larsen [30]
Task Graph Scheduling Task Graph Scheduling P 2 P 1 2 ,3 1 6 ,1 0 6 ,6 1 0 ,1 6 P 6 P 3 P 4 2 ,3 P 7 P 5 2 ,2 8 ,2 M = { M 1 ,M 2 } QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Guld Kim Guldstrand Larsen [31] Larsen [31]
Task Graph Scheduling Task Graph Scheduling P 2 P 1 2 ,3 1 6 ,1 0 6 ,6 1 0 ,1 6 P 6 P 3 P 4 2 ,3 P 7 P 5 2 ,2 8 ,2 M = { M 1 ,M 2 } E<> (Task1 End and E<> (Task1.End and … and Task7.End) and Task7 End) QMC, PhD School, March 3, QMC, PhD School, March 3, 2010 2010 Kim Guld Kim Guldstrand Larsen [32] Larsen [32]
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