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Stabilization

Stabilization. Consider nonmasking Fault-Tolerance. Invariant Fault-Span Program computation that starts from fault-span is guaranteed to reach invariant? What if Fault-span = set of all states? Such systems are called self-stabilizing. Defining stabilization.

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Stabilization

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  1. Stabilization

  2. Consider nonmasking Fault-Tolerance • Invariant • Fault-Span • Program computation that starts from fault-span is guaranteed to reach invariant? • What if Fault-span = set of all states? • Such systems are called self-stabilizing

  3. Defining stabilization • Starting from an arbitrary state, program eventually recovers to states from where subsequent computations are legitimate (i.e., meet the specification)

  4. Token ring stabilization problem • Two problem cases: • no token • several tokens • Both cases are hard to detect locally • how can we make them easier to detect and/or correct locally? 4

  5. Example • Consider a ring of processes 0..n • Each process has a variable x • Variable of j is x.j • Suppose x.j is an integer for now

  6. Actions • At process j, j > 0 • x.j ≠ x.(j-1)  x.j = x.(j-1) • At process 0 • x.0 = x.N  x.0 = x.N+1 • Let initial state be such that all x values are 0

  7. How does the execution proceed?

  8. What are legitimate states?

  9. What if faults change value of x? • Can we show that recovery will be guaranteed from an arbitrary state • Assume that no processes actually fail.

  10. What if we restrict domain of x? • Let x be from 0..M-1 • Change action at 0 as • x.0 = x.N  x.0 = (x.N+1) mod M • What if M =2 (Assume N is arbitrary) • What if M = N?

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