1. Discrete Simulation of Behavioural Hybrid Process Calculus Tomas Krilavičius Helen Shonenberg University of Twente

2. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 1 Outline Motivation Behavioural Hybrid Process Calculus Discrete simulation Future plans Conclusions Motivation Behavioural Hybrid Process Calculus Discrete simulation Future plans Conclusions

3. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 2 Motivation Formal languages Hybrid systems: embedded systems, models in natural and social sciences Main analysis technique for hybrid systems Formal languages Hybrid systems: embedded systems, models in natural and social sciences Main analysis technique for hybrid systems

4. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 3 Behavioural Hybrid Process Calculus Process algebraic theory concurrency, communication, discrete actions Process algebraic theory concurrency, communication, discrete actions Behavioural theory continuous realm J.W.Polderman, J.C.Willems Introduction to Mathematical Systems Theory Behavioural theory continuous realm J.W.Polderman, J.C.Willems Introduction to Mathematical Systems Theory

5. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 4 Behavioural Hybrid Process Calculus Trajectory-prefix Superposition Parallel composition Separation of concerns Bisimulation is congruence Trajectory-prefix Superposition Parallel composition Separation of concerns Bisimulation is congruence Trajectories and their continuations Choice is made when it is really time to do it Synchronisation on specified actions&signals Discrete and continuous behaviours can be separated syntactically Bisimilar processes can be substituted

6. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 5 Simulation of Hybrid Systems Main analysis technique for hybrid systems Discrete simulation Provides interesting information First step to simulation of hybrid systems

7. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 6 Discrete Simulation of BHPC Technique Application of SOS rules Expansion law Technique Application of SOS rules Expansion law Abstraction From Continuous Behaviour Trajectory-prefix Guard Superposition Parallel composition Abstraction From Continuous Behaviour Trajectory-prefix Guard Superposition Parallel composition

8. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 7 Trajectory-prefix Special type of action-prefix silent action special action to denote trajectory-prefix special action name for each trajectory-prefix Special type of action-prefix silent action special action to denote trajectory-prefix special action name for each trajectory-prefix

9. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 8 Guard false true assign evaluation for each guard individually

10. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 9 Superposition, Parallel Composition trajectory-prefix is treated as action-prefix trajectory-prefix is treated as action-prefix

11. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 10 Application of SOS

12. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 11 Expansion Law

13. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 12 Future Plans (I) Simulation of hybrid systems Simulation of continuous behaviour using ODE/DAE Solvers Resolving guard and parameterised action- prefix expressions Application of Expansion Law Simulation of hybrid systems Simulation of continuous behaviour using ODE/DAE Solvers Resolving guard and parameterised action- prefix expressions Application of Expansion Law

14. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 13 Future Plans (II) “Sand-box” tool playground for hybrid phenomena investigation testing algorithms changes in language (BHPC) co-simulation “Sand-box” tool playground for hybrid phenomena investigation testing algorithms changes in language (BHPC) co-simulation

15. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 14 Future Plans (III): Visualisation Process 1 Process 2 q1q2q3q1q2q3 □□□□□□ v v q1q2q4q1q2q4 □□□□□□ v v a1a1 a2a2 a3a3 a3a3 Message Sequence Charts for discrete behaviour Graphs for continuous behaviour

16. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 15 Future Plans (IV) Model-based testing Theory for model-based testing of hybrid systems Integration with TorX (H. Bohnenkamp & A. Belinfante. Timed testing with TorX. 2005) Model-based testing Theory for model-based testing of hybrid systems Integration with TorX (H. Bohnenkamp & A. Belinfante. Timed testing with TorX. 2005)

17. Tomas Krilavičius and Helen Schonenberg Discrete Simulation of BHPC 16 Conclusions Work in progress Abstractions of continuous behaviour Evaluation of Behavioural Hybrid Process Calculus Work in progress Abstractions of continuous behaviour Evaluation of Behavioural Hybrid Process Calculus