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

2. Message-Passing Model1 2 3 4
Network bidirectionnal and fully-connected
Communications by messages
Links asynchronous, fair, and FIFO
Ids on processes
Transient faults ma mb m3 m m2 m1 ma mb m3
08/04/2008
Orsay, séminaire

3. Stabilizing Protocols
Self-Stabilization [Dijkstra, 1974] c1 c2 c3 c4 c5 c6 c7
Convergence
time
correct behavior
uncorrect behavior
correct behavior
Transient Faults
Arbitrary initial state
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4. Stabilizing Protocols
Snap-Stabilization [Bui et al, 1999] c1 c2 c3 c4 c5 c6 c7
time
correct behavior
uncorrect behavior
correct behavior
Transient Faults
Arbitrary initial state
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5. Related Works in message-passing (reliable communication in self-stabilization)?
<How old are you, Captain?>
<I’m 21> ?
<I’m 60>
<I’m 12>
[Gouda & Multari, 1991]
Deterministic + Unbounded Capacity => Unbounded Counter
Deterministic + Bounded Capacity => Bounded Counter
[Afek & Brown, 1993]
Probabilistic + Unbounded Capacity + Bounded Counter
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6. Related Works in message-passing (self-stabilization)
[Varghese, 1993]
Deterministic + Bounded Capacity
[Katz & Perry, 1993]
Unbounded Capacity, deterministic, infinite counter
[Delaët et al]
Unbounded Capacity, deterministic, finite memory
Silent tasks
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7. Related Works (snap-stabilization)
Nothing in the Message-Passing Model
Only in State Model:
Locally Shared Memory
Composite Atomicity
[Cournier et al, 2003]
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8. Snap-Stabilization in Message-Passing Systems

9. Case 1: unbounded capacity links
Impossible for safety-distributed specifications
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10. Safety-distributed specificationq
Example : Mutual Exclusion
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11. Safety-distributed specificationm1 m2 m3 m4 m5 sq B q
m’1
m’2
m’3
m’4
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12. Safety-distributed specificationm1 m2 m3 m4 m5 sq B q
m’1
m’2
m’3
m’4
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13. Case 2: bounded capacity links
Problem to solve: Reliable Communication
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 ? ?
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14. Case 2: bounded capacity links
Case Study: Single-Message Capacity
0 or 1 message
0 or 1 message
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15. Case 2: bounded capacity links
Sequence number State  {0,1,2,3,4} p q
<1,NeigStatep,Qp,Ap>
<0,NeigStatep,Qp,Ap>
<Stateq,0,Qq,Aq>
Statep 1 ?
Until Statep = 4
Stateq ?
NeigStatep
NeigStateq ? ?
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16. Case 2: bounded capacity links
Pathological Case: p
<2,?,?,?>
<3,NeigStatep,Qp,Ap> q
<Stateq,3,Qq,Aq>
<?,2,?,?>
<?,1,?,?>
<?,0,?,?>
Statep
Stateq 1 4 2 3 ?
NeigStatep
NeigStateq ? 3 1 2
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17. Generalizations Arbitrary Bounded Capacity 2xCmax+3 values Cmax valuesq
Cmax values
1 value
1 value
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18. Generalizations PIF in fully-connected network m m Am m Am Am
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19. Application
Mutual Exclusion in a fully-connected & identified network using the PIF
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20. 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
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21. Principles (1/6) Let L be the process with the smallest ID
L decides using ValueL which is authorized to access the CS
if ValueL = 0, then L is authorized
if ValueL = i, then the ith neighbor of L is authorized
When a process learns that it is authorized by L to access the CS:
It ensures that no other process can execute the CS
It executes the CS, if it requests it
It notifies L when it terminates Step 2 (so that L increments ValueL)
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22. Principles (2/6)
Each process sequentially executes 4 phases infinitely often
A requesting process p can enter in the CS only after executing Phases 1 to 4 consecutively
The CS is in Phase 4
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23. Principles (3/6) Process p evaluates the IDs 5 3 8 2 Id? Id? 3 Id? 8 2
Phase=1 5 3
Leader=2
Id? 3
Id? 8 2 8 2
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24. Principles (4/6) Process p asks if Valueq = p to each other process q
Ok?
Phase=2 5 1
Leader=2 3
Ok=true No
Value=0
Ok? 2 3
Ok? No
Yes 1 2 1 2 8 2 3 3
Value=3
Value=2
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25. Principles (5/6)
If Winner(p) then p broadcasts EXIT to every other process
Winner(5)=true
Winner(3)=?
Exit
Phase=3
Phase=1
Phase=? 5 1 3
Leader=2
Leader=?
Exit Ok
Ok=true
Ok=? 2 3
Exit
Value=0
Winner(8)=?
Winner(2)=? Ok Ok
Phase=1
Phase=? 1
Phase=1
Phase=? 2 1
Leader=? 2
Leader=? 8 2
Ok=?
Ok=?
Value=3 3 3
Value=2
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26. Principles (6/6)
If Winner(p) then CS; If p≠L, then p broadcasts ExitCS, else p increments Valuep
Winner(5)=true
Winner(3)=?
ExitCS
<CS>
Phase=4
Phase=1 5 1 3
Leader=2
Leader=?
ExitCS Ok
Ok=?
Ok=true 2 3
Value=0
ExitCS
Winner(8)=?
Winner(2)=? Ok Ok
Phase=1 1
Phase=1 2 1
Leader=? 2
Leader=? 8 2
Ok=?
Ok=?
Value=3 3 3
Value=3
Value=2
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27. Snap-Stabilization in message-passing is no more an open question
Conclusion
Snap-Stabilization in message-passing is no more an open question
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28. Extensions Apply snap-stabilization in message-passing to:
Other topologies (tree, arbitrary topology)
Other problems
Other failure patterns
Space requirement
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29. Thank you