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Marco Realacci 2025-03-25 17:12:22 +01:00
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5
Concurrent Systems/notes/8 - Enhancing Liveness Properties.md
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@ -95,12 +95,13 @@ Forall i
$\Omega_{X}$ is not stronger than ♢P (so, ♢P is strictly stronger)
The formal proof consists in showing that if $\Omega_{X}$ was stronger than ♢P, then consensus would be possible in an asynchronous system with crashes and atomic R/W registers.
(because ♢P can solve consensus, )
(because ♢P can be used to solve consensus)
#### A contention manager for ♢P
We assume a weak timestamp generator, i.e. a function such that, if it returns a positive value t to some process, only a finite number of invocations can obtain a timestamp smaller than or equal to t
```
TS[1..n] : SWMR atomic R/W registers init at 0
...
need_help(i) :=
TS[i]
```