Timed Logics

  • View
    40

  • Download
    0

Embed Size (px)

DESCRIPTION

Logics & Preorders from logic to preorder – and back Kim Guldstrand Larsen Paul PetterssonMogens Nielsen BRICS@Aalborg BRICS@Aarhus. Timed Logics. Real-time temporal logic (RTTL, Ostroff and Wonham 85) Metric Temporal Logic (Koymans, 1990) - PowerPoint PPT Presentation

Text of Timed Logics

  • Logics & Preorders from logic to preorder and back

    Kim Guldstrand Larsen Paul PetterssonMogens Nielsen BRICS@Aalborg BRICS@Aarhus

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Timed Logics .....Real-time temporal logic (RTTL, Ostroff and Wonham 85)Metric Temporal Logic (Koymans, 1990)Explicit Clock Temporal Logic (Harel, Lichtenstein, Pnueli, 1990)Timed Propositional Logic (Alur, Henzinger, 1991)

    Timed Computational Tree Logic (Alur, Dill, 1989)Timed Modal Mu-Calculus (Larsen, Laroussinie, Weise, 1995)

    Duration Calculus (Chaochen, Hoare, Ravn, 1991)

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Timed Modal Logic Atomic PropRecursion VariablesActionModalitiesBoolean ConnectivesKozen83

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Timed Modal Logic Atomic PropRecursion VariablesActionModalitiesBoolean ConnectivesFormulaClockConstrFormulaClockResetDelayModalitiesLarsen, Laroussine, Weise, 1995Larsen, Pettersson, Wang, 1995Larsen, Holmer, Wang91

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Semanticsstate of timed automatatimed asgnfor formula clocksformulaSemantics

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Derived Operatorsf holds between l and uInvariantlyWeak UNTILBounded UNTILTimed Modal Mu-calculusis at least as expressiveas TCTL

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Symbolic Semanticslocationregion over C and KformulaRegion-based SemanticsTHEOREM

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Fundamental Results Given f does there exist an automaton A satisfying f ? Given f and given clock-set C and max constant M. Does there exist an automaton A over C and M satisfying f ? UNDECIDABLE(strong conjecture)Decidable Given f and automaton A does A satisfy f ? Decidable

    EXPTIME-complete(Aceto,Laroussinie99)

  • Timed BimulationWang91, Cerans92

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Timed BisimulationWang91

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Timed Simulation

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Examples

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Towards Timed Bisimulation Algorithmindependentproduct-constructionCerans92

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Towards Timed Bisimulation AlgorithmDefinitionTheorem

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Timed Bisimulation Algorithm = Checking for TB-ness using RegionsxyAX,R0AX,R1AX,R2AY,R3a2a1112

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Characteristic Propertyfor finite state automataa1aknm1mkLarsen, Ingolfsdottir, Sifakis, 1987Ingolfsdottir, Steffen, 1994

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Characteristic Propertyfor finite state automataa1aknm1mkLarsen, Ingolfsdottir, Sifakis, 1987Ingolfsdottir, Steffen, 1994

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Characteristic Propertyfor timed automataa1aknm1mkg1r1gkrkInv(n)IDEA_ Automata clocks become formula clocksLarsen, Laroussinie, Weise, 1995

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Characteristic Propertyfor timed automataa1aknm1mkg1r1gkrkInv(n)IDEA_ Automata clocks become formula clocksLarsen, Laroussinie, Weise, 1995

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Timed Bisimulation as a formula

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Timed Safety LogicBack to Zones Atomic PropRecursion VariablesActionModalitiesBoolean ConnectivesFormulaClockConstrFormulaClockResetDelayModalitiesLarsen, Pettersson, Wang, 1995

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Zone Semanticslocationzoneover C and KformulaMC wrt Safety Logicis PSPACE complete

    UCb Petri Net, June 2000Kim G. Larsen, Mogens Nielsen, Paul Pettersson

    Characteristic Property/Simulationfor deterministic timed automataaanm1mkg1r1gkrkInv(n)Aceto, Burgueno,Bouyer, Larsen, 1998gi and gj = determinism

  • END

    Formal Methods Automatic Validation and Verification Tools

    Kim Guldstrand LarsenBRICS@AalborgInstitute of Computer ScienceAalborg University

    Formal Methods seems to be finding its way into industrial software engineering practice. In particular, methods based on fully automatic verification tools have for a long time been established practice for hardware designs.

    Today, an increasing number of (commercial) tools offering automatic verification support for industrial designs of embedded systems, real-time systems, and communication protocols are emerging. The scalability of these tools has been significantly improved due to recent, scientific advances in the underlying algorithmic techniques, which have allowed for large industrial applications to be verified.

    The talk will present the tool UPPAAL, a tool suite for validating and verifying real-time system models. The tool has been developed since 1995 in collaboration between Aalborg and Uppsala Universities. The presentation will be based on on-line demonstration and survey the industrial applications of UPPAAL.

    The final part of the talk will address the tool visualSTATE, a commercial tool for automatic validation and verification of embedded system models In addition visualSTATE allows for automatic generation of efficient code for a number of platforms. Resent collaboration between visualSTATE, BRICS@Aalborg and DTU has resulted in truely significant advances in the size of systems which may be dealt with.