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1 Hybrid Systems from timed automata to hybrid systems – and back Kim Guldstrand Larsen Paul PetterssonMogens Nielsen nearly

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 2 Vending Machine 1 Timed Automata

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 3 Vending Machine 1 Timed Automata time x cupdel-cof ord-cof Behaviour

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 4 Vending Machine 2 Hybrid Automata Maler, Manna, Pnueli’91 Clocks -> Continuous Variables

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 5 Vending Machine 2 Hybrid Automata t cupdel-coford-cof Behaviour T,HT,H Maler, Manna, Pnueli’91 Clocks -> Continuous Variables

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 6 Vending Machine 3 Linear Hybrid Automata Alur, Courcouretis, Henzinger, Ho’93

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 7 Vending Machine 3 t cupdel-coford-cof Behaviour T,HT,H Linear Hybrid Automata Alur, Courcouretis, Henzinger, Ho’93 HYTECH

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 8 Symbolic Analysis Polyhedra H T

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 9 Symbolic Analysis Polyhedra H T

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 10 Symbolic Analysis Polyhedra H T

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 11 Symbolic Analysis Polyhedra H T The exploration may lead to generation of infinitely many polyhedra => No guarantee of termination Manipulation of polyhedra inefficient!

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 12 TA’s versus LHA’s zTOOLS yUPPAAL, KRONOS,CMC,... zDecidable zEfficient Datastructure yDBM’s, NDD’s, CDD’s,.. zExpressiveness zTOOLS yHYTECH, POLLUX,.. zUndecidability zDatastructures yPlyhedra zExpressiveness STOPWATCH AUTOMATA x’==0 or x’==1

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UCb Petri Net June, 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson 13 STOPWATCH AUTOMATA zExtension of UPPAAL to SWA yReuse of efficient datastructures yOverapproximation zEvery LHA may be translated into a SWA zAPPLICATIONS yScheduler yGasburner yWater Level Control Cassez, Larsen, CONCUR’00

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