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Concurrent Systems/notes/8 - Enhancing Liveness Properties.md
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@ -71,11 +71,11 @@ IDEA:
- this changes in time, but not forever (can be proved, but it's not covered here) - this changes in time, but not forever (can be proved, but it's not covered here)
Guessing the time duration for suspecting a process: Guessing the time duration for suspecting a process:
- `SUSPECT[i,j]` = # of times pi has suspected pj - `SUSPECT[i,j]` = # of times $p_i$ has suspected $p_j$
- For all k, take the t+1 minimum values in `SUSPECT[1..n , k]` - For all k, take the t+1 minimum values in `SUSPECT[1..n , k]`
- remember: t is the max number of processes that can fail (it is known) - remember: t is the max number of processes that can fail (it is known)
- so doing this we ensure considering at least a process that doesn't fail - so doing this we ensure considering at least a process that doesn't fail
- Sum them, to obtain $S_{k}$ - Sum them, to obtain $S_{k}$ (for each process k)
- The interval to use in the timers is the minimum $S_{k}$ - The interval to use in the timers is the minimum $S_{k}$
- it can be proved that this eventually becomes ≥ $\nabla$ - it can be proved that this eventually becomes ≥ $\nabla$