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Concurrent Systems/notes/6 - Atomicity.md
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@ -49,7 +49,9 @@ We now show that $\to$ is acyclic.
3. It cannot have cycles with more than 2 edges: 3. It cannot have cycles with more than 2 edges:
- by contradiction, consider a shortest cycle - by contradiction, consider a shortest cycle
- adjacent edges cannot belong to the same order (not both $\to_X$ ), otw. the cycle would be shortable, because of transitivity of the total order! - adjacent edges cannot belong to the same order (e.g. not both $\to_X$), otw. the cycle would be shortable, because of transitivity of the total order!
- adjacent edges cannot belong to orders on different objects
- this would mean that an operation is involved in both $\to_X$ and $\to_Y$
> [!PDF|red] class 6, p.6> we would have a cycle of length > [!PDF|red] class 6, p.6> we would have a cycle of length