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Real-Time Synchronised Petri Nets

Real-Time Synchronised Petri Nets. Giovanna Di Marzo Serugendo Dino Mandrioli, Didier Buchs, Nicolas Guelfi University of Geneva, Switzerland. PN’02 / 24th June 2002. Giovanna Di Marzo Serugendo. Motivations. Synchronised Petri Nets CO-OPN Real-Time

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Real-Time Synchronised Petri Nets

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  1. Real-Time Synchronised Petri Nets Giovanna Di Marzo Serugendo Dino Mandrioli, Didier Buchs, Nicolas Guelfi University of Geneva, Switzerland PN’02 / 24th June 2002 Giovanna Di Marzo Serugendo

  2. Motivations • Synchronised Petri Nets • CO-OPN • Real-Time • Time interval attached to transitions • Inhibitor Arcs • Maximum number of tokens in place • Real-Time Synchronised Petri Nets

  3. Synchronised Petri nets • Concurrent Object-Oriented Petri Nets • Object-Orientation • External and Internal Transitions • Synchronisation Requests • simple • simultaneity, sequence, alternative operators • transactional semantics (all or nothing) • Abstract Data Types • This paper: • Object-based • Time stamped mono colored token

  4. Real-Time • Time Interval • Attached to each transition • Merlin-Farber model • Instantaneous firing • Time of Firing: • Bound by time interval in R+ • Relative to time when transition becomes enabled

  5. Time Interval Synchronisation Methods move [5..15] put [2..10] 1 Transition processing [1..9] 1 0 1 0 0 0 p1 p2 O1 O2 Objects Real-Time Synchronised Petri Nets

  6. move [5..15] put [2..10] 1 processing [1..9] 1 0 1 X 5 0 0 0 p1 p2 O1 O2 Real-Time Synchronised Petri Nets

  7. move [5..15] put [2..10] 1 processing [1..9] 1 0 1 X 0 0 5 0 p1 p2 O1 O2 Real-Time Synchronised Petri Nets

  8. move [5..15] put [2..10] 1 processing [1..9] 1 0 1 0 0 7 0 p1 p2 O1 O2 Real-Time Synchronised Petri Nets

  9. Semantics • How to deal with: • Merlin-Farber and Synchronisations • Firing respecting Time interval • Tokens production time • Synchronisation • Intersection of time intervals for simultaneity • Correct time of production of tokens for sequence • Non-determinism in the case of alternative • Inhibitor Arcs • Ensure inhibitor arc condition even with chains of synchronisations

  10. Semantics • Structured Operational Semantics Rules (SOS) • 4 Steps • Weak Transition System • Strong Transition System • Expanded Transition System (Synchronisation) • Observable Strong Time Semantics • paths starting from initial marking

  11. Transition System • Events • Methods and Transitions • Synchronisation /Simultaneous / Sequence / Alternative • Markings • Time Stamped Tokens • Time of Firing 2

  12. Weak Transition System • Single Firings • synchronisation is not taken into account • time of firing occurs in time interval • inhibitor arc condition is verified • post-condition produces tokens stamped at time of firing • Elapsed Time Interval • does not impose transition firing at maximal bound of interval

  13. put [2..10] move [5..15] 1 1 0 processing [1..9] 1 X 0 0 0 p1 p2 O1 O2 SOS Rules 5

  14. Strong Transition System • Elapsed Time Interval • Transition has to fire • Remove transitions that prevent other transitions to fire when time elapses • Two transitions reaching maximal bound of firing at the same time: • both are allowed • one may still disable the other

  15. Expanded Transition System • Synchronisation • move and put must fire at the same time • result takes into account both firings • Observable Transition: only move • Simultaneity • Both transitions occur at the same time • Observable Transition: e1 // e2

  16. Expanded Transition System • Sequence • Transition e1 fires before e2 (t1 < t2) • Observable transition: e1 .. e2 • Tokens stamped at t1 and t2 • Tokens stamped at t2: not available before t2 • Alternative • Transition e1 or transition e2 fires at t • Observable transition: e1 + e2 • Tokens stamped at t • Result: due to e1 or e2

  17. 5 5 5 Synchronisation

  18. Strong Time Semantics • Retain observable transitions reachable from initial marking • Time increases • Semantics = paths of transitions starting from initial marking

  19. ... {0,0},{6} put,6 {0,0},{5} {0,0},{} ... {0},{6} move,5 processing,6 move,6 move + put,5.5 {0,0},{5.5} ... put,2 ... ... {0,0,0},{2} {0,0,0},{} ... processing,3 Strong Time Semantics {0,0,0},{} time

  20. Train • Railroad Crossing System • Specification • Trains • Level Crossing • Safety and Utility Properties • determination of time needed to operate the bar

  21. Conclusion • Syntax and Semantics of Real-time Synchronised Petri Nets • Towards: • Object-Oriented Real-Time Petri Nets • True Operational Semantics already realised • first step towards reachability analysis • Future Work • Axiomatisation: formal verification of properties

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