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7
Concurrent Systems/notes/6 - Atomicity.md
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@ -56,8 +56,11 @@ We now show that $\to$ is acyclic.
- can this be a cycle? - can this be a cycle?
- $op1 \to_H op2$ means that $res(op1) <_H inv(op2)$ - $op1 \to_H op2$ means that $res(op1) <_H inv(op2)$
- $op2 \to_X op3$ entails that $inv(op2) <_H res(op3)$ - $op2 \to_X op3$ entails that $inv(op2) <_H res(op3)$
- if not, as is a total order, we would have that $res(op3) <_H inv(op2)$, but we then would have $op3 \to_H op2$ a cycle of lenght 2... - if not, as is a total order, we would have that $res(op3) <_H inv(op2)$, but we then would have $op3 \to_H op2$, forming a cycle of lenght 2 because $op2 \to_X op3$, and we know cycles of lenght 2 are not possible...
- $op2 \to_H op3$ entails that $inv(op2) <_H res(op3)$ - $op3 \to_H op4$ means that $res(op3) <_H inv(op4)$
- We would then have that $res(op1) <_H inv(op2) <_H res(op3) <_H inv(op4)$
- So by transitivity $res(op1) <_H inv(op4)$
> [!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