1. Snap-Stabilization in Message-Passing Systems Sylvie Delaët (LRI) Stéphane Devismes (CNRS, LRI) Mikhail Nesterenko (Kent State University) Sébastien Tixeuil (LIP6)

2. 07/02/2008Séminaire "Algorithmique Répartie", LIP62 Preliminaries

3. 07/02/2008Séminaire "Algorithmique Répartie", LIP63 From an arbitrary initial configuration? (after some transient failures) ? ? + unreliable asynchronous but FIFO links (induces problems of duplicates)

4. 07/02/2008Séminaire "Algorithmique Répartie", LIP64 Solutions Self-Stabilization [Dijkstra 1974]: Starting from any configuration, the protocol resumes a correct behavior in finite time Starting from any configuration, If Tintin sends infinitely many questions to Captain Haddock, then: Tintin receives infinitely many good answers Tintin eventually only takes the good answers into account

5. 07/02/2008Séminaire "Algorithmique Répartie", LIP65 Solutions Snap-Stabilization [Bui et al,1999]: Starting from any configuration, every computation of the protocol that is started returns a correct result Starting from any configuration, if Tintin sends a question to Captain Haddock, then: Tintin eventually receives good answers Tintin takes only the good answers into account

6. 07/02/2008Séminaire "Algorithmique Répartie", LIP66 Related Works (reliable communication in self-stabilization) [Gouda & Multari, 1991]  Deterministic + Unbounded Capacity => Infinite Counter  Deterministic + Bounded Capacity => Finite Counter [Afek & Brown, 1993]  Probabilistic + Unbounded Capacity + Finite Counter

7. 07/02/2008Séminaire "Algorithmique Répartie", LIP67 Related Works (self-stabilization in message-passing) [Varghese, 1993]  Deterministic + Bounded Capacity [Katz & Perry, 1993]  Unbounded Capacity, deterministic, infinite counter [Delaët et al]  Unbounded Capacity, deterministic, finite memory  Silent tasks

8. 07/02/2008Séminaire "Algorithmique Répartie", LIP68 Related Works (snap-stabilization) Nothing in the Message-Passing Model Only in State Model:  Locally Shared Memory  Composite Atomicity [Cournier et al, 2003]

9. Snap-Stabilization in Message-Passing Systems

10. 07/02/2008Séminaire "Algorithmique Répartie", LIP610 Case 1: unbounded capacity links Impossible for safety-distributed specifications  E.g. Mutual Exclusion

11. 07/02/2008Séminaire "Algorithmique Répartie", LIP611 Case Study: Mutual Exclusion Specification of the Mutual Exclusion:  Any process that requests the CS enters in the CS in finite time (Liveness)  If a requesting process enters in the CS, then it executes the CS alone (Safety) N.b. Some non-requesting processes may be initially in the CS

12. 07/02/2008Séminaire "Algorithmique Répartie", LIP612 Case Study: Mutual Exclusion Let p, q be two distinct processes p q q p q p

13. 07/02/2008Séminaire "Algorithmique Répartie", LIP613 Case 2: bounded capacity links Case Study: Single-Message Capacity 0 or 1 message

14. 07/02/2008Séminaire "Algorithmique Répartie", LIP614 Case 2: bounded capacity links Sequence number State  {0,1,2,3,4} p q State p State q 0 NeigState p NeigState q ? ?? 0 1 Until State p = 4

15. 07/02/2008Séminaire "Algorithmique Répartie", LIP615 Case 2: bounded capacity links Pathological Case: p q State p State q 0 NeigState p NeigState q ? 1? 1 2 2 3 3 4

16. 07/02/2008Séminaire "Algorithmique Répartie", LIP616 Generalizations Arbitrary Bounded Capacity PIF in fully-connected network

17. 07/02/2008Séminaire "Algorithmique Répartie", LIP617 Application Mutual Exclusion in a fully-connected & identified network using the PIF

18. 07/02/2008Séminaire "Algorithmique Répartie", LIP618 Mutual Exclusion Specification:  Any process that requests the CS enters in the CS in finite time (Liveness)  If a requesting process enters in the CS, then it executes the CS alone (Safety) N.b. Some non-requesting processes may be initially in the CS

19. 07/02/2008Séminaire "Algorithmique Répartie", LIP619 Principles (1/3) Let L be the process with the smallest ID L decides using Value L which process can enter in the CS When a process learns that it is authorized by L to access the CS: 1.It ensures that no other process can execute the CS 2.It executes the CS, if it requests it 3.It notifies the leader when it terminates Step 2

20. 07/02/2008Séminaire "Algorithmique Répartie", LIP620 Principles (2/3) Each process sequentially executes 4 phases infinitely often A requesting process can enter in the CS only after executing Phases 1 to 3

21. 07/02/2008Séminaire "Algorithmique Répartie", LIP621 Principles (3/3) For a process p: Phase 1: p evaluates the IDs using a PIF Phase 2: p asks if Value q = p to each other process q (PIF) Phase 3: If Winner(p) then p broadcasts EXIT to every other process (PIF) Phase 4: If Winner(p) then CS; p broadcasts EXITCS (PIF)

22. 07/02/2008Séminaire "Algorithmique Répartie", LIP622 Conclusion Snap-Stabilization in message-passing is no more an open question

23. 07/02/2008Séminaire "Algorithmique Répartie", LIP623 Extension Apply snap-stabilization in message-passing to:  Other topologies  Other problems  Other failure patterns

24. Thank you