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Marco Realacci 2025-03-25 17:12:22 +01:00
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8
.obsidian/workspace.json vendored
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@ -6,7 +6,7 @@
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"Concurrent Systems/notes/7- MUTEX-free concurrency.md",
"Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",
"Concurrent Systems/slides/class 8.pdf", "Concurrent Systems/slides/class 8.pdf",
"Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",
"Concurrent Systems/notes/7- MUTEX-free concurrency.md",
"Concurrent Systems/slides/class 7.pdf", "Concurrent Systems/slides/class 7.pdf",
"Concurrent Systems/notes/6a - Alternatives to Atomicity.md", "Concurrent Systems/notes/6a - Alternatives to Atomicity.md",
"Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md", "Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md",

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) $\Omega_{X}$ 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. 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 #### 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 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 TS[1..n] : SWMR atomic R/W registers init at 0
... need_help(i) :=
TS[i]
``` ```