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Yury Chebiryak chebiryak@mail.ru

University of Saarland Department of Computer Science. Formal. Specification and Verification of. Functions of the. VAMOS Scheduler. Yury Chebiryak chebiryak@mail.ru. Master’s Seminar. 19.07.2005. Overview. VAMOS configuration Assumptions Functional Verification Specification

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Yury Chebiryak chebiryak@mail.ru

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  1. University of SaarlandDepartment of Computer Science Formal Specification and Verification of Functions of the VAMOS Scheduler Yury Chebiryak chebiryak@mail.ru Master’s Seminar 19.07.2005

  2. Overview • VAMOS configuration • Assumptions • Functional Verification • Specification • Proof Sketch • Invariants

  3. VAMOS Configuration

  4. VAMOS configuration: gd

  5. VAMOS configuration: PrcsConf

  6. VAMOS Scheduler

  7. Overview • VAMOS configuration • Assumptions • Functional Verification • Specification • Proof Sketch • Invariants

  8. vamosData

  9. vamosData • Disjointness of lists of VAMOS • Current process is always ready

  10. vamosData • Always exist at least one ready process (IDLE) • Length of ReadyListsArray • Priority is in correct range

  11. vamosData • Current Maximum Priority (CMP) is in correct range • Ready List indexed by CMP is not empty • Current maximum priority is correct

  12. Overview • VAMOS configuration • Assumptions • Functional Verification • Specification • Proof Sketch • Invariants

  13. Specification: search_next_process Signature: Assumptions: Let Result:

  14. Specification: compute_max_prio Signature: Assumptions: Let Result:

  15. Specification: wake_up

  16. Specification: wake_up

  17. Specification: wake_up

  18. Specification: wake_up

  19. Specification: wake_up Signature: Let Assumptions: Let

  20. Specification: wake_up Result:

  21. Specification: process_get_mypid Signature: Assumptions: Result:

  22. Specification: process_switch_to

  23. Specification: process_switch_to

  24. Specification: process_switch_to

  25. Specification: process_switch_to

  26. Specification: process_switch_to Signature: Assumptions: Let

  27. Specification: process_switch_to Abbreviations:

  28. Specification: process_switch_to Result(1):

  29. Specification: process_switch_to Result(2): Error Result:

  30. Specification: prcs_ch_sch_p Signature: Assumptions:

  31. Specification: prcs_ch_sch_p Let

  32. Specification: prcs_ch_sch_p Let Error Result:

  33. Specification: prcs_ch_sch_p Result:

  34. Overview • VAMOS configuration • Assumptions • Functional Verification • Specification • Proof Sketch • Invariants

  35. Proof Sketch: wake_up int wake_up(pib_p p) { pib_p dummy; int dummy_int; wakeup_list = dlist_pib_t_queue_Delete(wakeup_list,p); ready_lists[p->priority] = queue_InsertTail(ready_lists[p->priority],p); p->state = VAMOS_PROCESS_READY; if (p->priority > current_max_prio) { current_max_prio = p->priority; dummy_int = search_next_process(); } return 0; }

  36. Proof Sketch: wake_up int wake_up(pib_p p) { pib_p dummy; int dummy_int; wakeup_list = dlist_pib_t_queue_Delete(wakeup_list,p); ready_lists[p->priority] = queue_InsertTail(ready_lists[p->priority],p); p->state = VAMOS_PROCESS_READY; if (p->priority > current_max_prio) { current_max_prio = p->priority; dummy_int = search_next_process(); } return 0; }

  37. Proof Sketch: wake_up int wake_up(pib_p p) { pib_p dummy; int dummy_int; wakeup_list = dlist_pib_t_queue_Delete(wakeup_list,p); ready_lists[p->priority] = queue_InsertTail(ready_lists[p->priority],p); p->state = VAMOS_PROCESS_READY; if (p->priority > current_max_prio) { current_max_prio = p->priority; dummy_int = search_next_process(); } return 0; }

  38. Overview • VAMOS configuration • Assumptions • Functional Verification • Specification • Proof Sketch • Invariants

  39. Invariants: Safety properties • Proceses from wakeup_list are not scheduled • After call of search_next_process current process has priority current_max_prio • If process i has priority less than current_max_prio it can only be scheduled if switch_to(i) is invoked (not by handler_clock)

  40. Invariants: Safety properties • If during execution of process i there was no call of wake_up of process with priority higher than current_max_prio, then process i consumes its whole timeslice (it will not be interrupted) • If there is only one process with priority current_max_prio, then it will run until • call of switch_to() or • call of process_kill performing suicide or • wake_up of process with higher priority.

  41. Invariants: Liveness properties • Processes with current_max_prio share CPU time with respect to their timeslices

  42. Summary

  43. Thank you. Questions?

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