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13
Concurrent Systems/notes/6 - Atomicity.md
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@ -2,4 +2,15 @@ We have a set of n sequential processes $p_{1},...,p_n$ , that access $m$ concur
When invoked by $p_j$, the invocation `Xi.op(args)(ret)` is modeled by two events: `inv[Xi.op(args) by pj]` and `res[Xi.op(ret) to pj]`.
A **history** (or **trace**) is a pair $\hat{H}=(H, <_{H})$ where H is a set of events and $<_{H}$ is a total order on them.
A **history** (or **trace**) is a pair $\hat{H}=(H, <_{H})$ where $H$ is a set of events and $<_{H}$ is a total order on them.
The *semantics* (of systems and/or objects) will be given as the set of traces.
A history is **sequential** if it is of the form `inv res inv res ... inv res inv inv inv ...`, where every res is the result of the immediately preceding inv. (The last invocations do not have a return).
A sequential history can be represented as a sequence of operations.
A history is **complete** if every inv is eventually followed by a corresponding res, it is **partial** otherwise.
### Linearizability
A complete history $\hat{H}$ is **linearizable** if there exists a sequential history $\hat{S}$ s.t.
- $f$