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COLE SUPRIEURE DLECTRICIT Semantic Adaptation for Models of Computation ACSD 2011 in Newcastle Frdric Boulanger Ccile Hardebolle, Christophe Jacquet, Dominique Marcadet Suplec E3S Computer Science Department June 24

  1. ÉCOLE Semantic adaptation SUPÉRIEURE D’ÉLECTRICITÉ Example : power window DE bus Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 14 / 22

  2. ÉCOLE Semantic adaptation SUPÉRIEURE D’ÉLECTRICITÉ Example : power window TFSM DE bus Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 14 / 22

  3. ÉCOLE Semantic adaptation SUPÉRIEURE D’ÉLECTRICITÉ Example : power window TFSM SDF DE bus Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 14 / 22

  4. ÉCOLE Semantic adaptation SUPÉRIEURE D’ÉLECTRICITÉ Example : power window TFSM SDF ? ? DE bus Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 14 / 22

  5. ÉCOLE Semantic adaptation (data) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of data between DE and TFSM value symbol date Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 15 / 22

  6. ÉCOLE Semantic adaptation (data) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of data between DE and TFSM symbol = f ( value ) value symbol date Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 15 / 22

  7. ÉCOLE Semantic adaptation (data) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of data between DE and TFSM symbol = f ( value ) value symbol value = g ( symbol ) date date = DE.now Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 15 / 22

  8. ÉCOLE Semantic adaptation (data) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of data between DE and TFSM symbol = f ( value ) value symbol value = g ( symbol ) date date = DE.now TFSM motor_stop 0 cmd_neutral 0 cmd_up motor_up cmd 1 1 motor -1 cmd_down motor_down -1 Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 15 / 22

  9. ÉCOLE Semantic adaptation (data) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of data between DE and SDF 0 2 1 DE t 0 t 1 t 2 SDF Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 16 / 22

  10. ÉCOLE Semantic adaptation (data) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of data between DE and SDF 0 2 1 DE t 0 t 1 t 2 SDF • Relative position of events / samples ⇒ adaptation of time • Presence of samples ⇒ adaptation of control Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 16 / 22

  11. ÉCOLE Semantic adaptation (data) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of data between DE and SDF 0 2 1 DE t 0 t 1 t 2 SDF 1 0 2 1 t 0 t 1 t 2 t 3 Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 16 / 22

  12. ÉCOLE Semantic adaptation (time) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of time Time in DE • Time stamps in R × N • Synchronization, causality • Controls when events are processed Time in TFSM • Measure of the elapsed time in a state • Time stamps have no special meaning Adaptation DE – TFSM • Mapping from TFSM durations to differences between DE time stamps • Consequences on control Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 17 / 22

  13. ÉCOLE Semantic adaptation (time) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of time Time in DE • Time stamps in R × N • Synchronization, causality • Controls when events are processed Time in SDF • Series of samples, no real notion of date • No notion of duration Adaptation DE – SDF • Give a DE time stamp to SDF data samples • Sampling period, consequences on control Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 17 / 22

  14. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control TFSM DE SDF Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  15. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control TFSM DE SDF Event in DE, no input for the state machine Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  16. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control TFSM DE SDF T T Periodic control for SDF Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  17. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control TFSM DE SDF T T Periodic control for SDF ⇒ control in DE Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  18. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control TFSM DE SDF T T Event in DE, input for the state machine ⇒ control in TFSM Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  19. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control ∆ T TFSM DE SDF T T Firing of a timed transition in the state machine Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  20. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control ∆ T TFSM DE SDF T T Firing of a timed transition in the state machine ⇒ control in DE Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  21. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control ∆ T TFSM DE SDF T T Periodic observation of SDF ⇒ control in DE + event for the state machine ⇒ control in TFSM Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  22. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control ∆ T TFSM DE SDF T T Data never creates control for SDF Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  23. ÉCOLE Semantic adaptation (control) SUPÉRIEURE D’ÉLECTRICITÉ Adaptation of control ∆ T TFSM DE SDF T T Data never creates control for SDF ⇒ data is memorized at the DE-SDF interface Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 18 / 22

  24. ÉCOLE Semantic adaptation SUPÉRIEURE D’ÉLECTRICITÉ Today • Adaptation of data: configurable semantic adaptation patterns • Adaptation of time: ad hoc handling in interface blocks • Adaptation of control: constraints on the date of the next snapshot The future • Adaptation of data: special MoC? • Adaptation of time and control: clock calculus (Clock Constraint Specification Language) Semantic Adaptation for Models of Computation Semantic adaptation June 24 2011 19 / 22

  25. ÉCOLE Plan SUPÉRIEURE D’ÉLECTRICITÉ 1 Introduction 2 Languages and models of computation 3 Semantic adaptation 4 Conclusion Semantic Adaptation for Models of Computation Conclusion June 24 2011 20 / 22

  26. ÉCOLE SUPÉRIEURE Conclusion D’ÉLECTRICITÉ Multi-paradigm modeling • Accept heterogeneity • Handle heterogeneity at the modeling level • Many special purpose tools (Simulink, System C-AMS) Our approach • Unifying syntax for heterogeneous models • Definition of models of execution • Explicit description of the semantic adaptation between models Key points • Well defined semantics for models and combinations of models • Joint use of already existing tools • Modularity (black box approach) Semantic Adaptation for Models of Computation Conclusion June 24 2011 21 / 22

  27. ÉCOLE SUPÉRIEURE D’ÉLECTRICITÉ Thanks for your attention Questions? Semantic Adaptation for Models of Computation Conclusion June 24 2011 22 / 22

  28. ÉCOLE Appendix SUPÉRIEURE D’ÉLECTRICITÉ Thermostat Fuse Snapshot with non-strict blocks Super dense time Snapshot computation Semantic Adaptation for Models of Computation Appendix June 24 2011 23 / 22

  29. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle ¯ x [ 2 ] Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  30. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle ¯ x [ 2 ] StartOfSnapshot Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  31. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle ¯ x [ 2 ] Schedule → ramp Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  32. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle 1 ¯ x [ 2 ] Update ramp Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  33. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle 1 ¯ x [ 2 ] Propagate Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  34. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle 1 ¯ x [ 2 ] Schedule → ramp Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  35. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle 2 1 ¯ x [ 2 ] Update ramp Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  36. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle 2 1 ¯ x [ 2 ] Propagate Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  37. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle 2 1 ¯ x [ 2 ] Schedule → average Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  38. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle 1.5 ¯ x [ 2 ] Update average Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  39. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle 1.5 ¯ x [ 2 ] Propagate Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  40. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle 1.5 ¯ x [ 2 ] Schedule → display Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  41. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle ¯ x [ 2 ] Update display Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  42. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle ¯ x [ 2 ] Done Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  43. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle ¯ x [ 2 ] Validate Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  44. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous data flow MoC • Instantaneous propagation of data • Consumption and production of a fixed number of data samples • Snapshot = shortest production/consumption cycle ¯ x [ 2 ] EndOfSnapshot Semantic Adaptation for Models of Computation Appendix June 24 2011 24 / 22

  45. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known A B Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  46. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 1 A B 0 StartOfSnapshot Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  47. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 1 A B 0 Schedule → A Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  48. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known ? 1 A B 0 Update A Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  49. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 1 A B 0 Schedule → B Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  50. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 1 A B 0 1 Update B Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  51. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 1 A 1 B 0 1 Propagate Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  52. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 1 A 1 B 0 1 Schedule → A Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  53. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 0 1 A 1 B 0 1 Update A Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  54. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 0 1 A 1 0 B 0 1 Propagate Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  55. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 0 1 A 1 0 B 0 1 Schedule → B Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  56. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 0 1 A 1 0 B 0 1 Update B Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  57. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 0 1 A 1 0 B 0 1 Done Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  58. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 0 1 A 1 0 B 0 1 Validate Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  59. ÉCOLE Example of computation of a snapshot SUPÉRIEURE D’ÉLECTRICITÉ Synchronous reactive MoC • Instantaneous propagation of data • Non-strict blocks (may react to partial inputs) • Snapshot = all signals are known 0 1 A 0 1 0 B 0 1 EndOfSnapshot Semantic Adaptation for Models of Computation Appendix June 24 2011 25 / 22

  60. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ Semantic Adaptation for Models of Computation Appendix June 24 2011 26 / 22

  61. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C State = heating Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  62. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C ∆ T State = heating ∆ T determined according to the precision on T Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  63. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C State = heating Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  64. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C State = heating Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  65. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C State = heating Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  66. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C ∆ T > ε State = heating The upper threshold is reached, but we don’t know when. The snapshot is not valid Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  67. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C State = heating Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  68. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C ∆ T < ε State = heating The upper threshold is reached, the date is precise enough. State changes Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  69. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C State = cooling Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  70. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C ∆ T > ε State = cooling Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  71. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C State = cooling Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  72. ÉCOLE Example of non validation in CT SUPÉRIEURE D’ÉLECTRICITÉ 21°C 20°C 19°C 18°C 17°C 16°C 15°C Semantic Adaptation for Models of Computation Appendix June 24 2011 27 / 22

  73. ÉCOLE Snapshot computation with non validation SUPÉRIEURE D’ÉLECTRICITÉ 1A U U U U 6 Ω 12V I I I I Semantic Adaptation for Models of Computation Appendix June 24 2011 28 / 22

  74. ÉCOLE Snapshot computation with non validation SUPÉRIEURE D’ÉLECTRICITÉ 1A U U U U 6 Ω 12V I I I I Schedule → battery Semantic Adaptation for Models of Computation Appendix June 24 2011 28 / 22

  75. ÉCOLE Snapshot computation with non validation SUPÉRIEURE D’ÉLECTRICITÉ 1A U U U U 12V 6 Ω 12V I I I I Update battery Semantic Adaptation for Models of Computation Appendix June 24 2011 28 / 22

  76. ÉCOLE Snapshot computation with non validation SUPÉRIEURE D’ÉLECTRICITÉ 1A U U U U 12V 12V 6 Ω 12V I I I I Propagate Semantic Adaptation for Models of Computation Appendix June 24 2011 28 / 22

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