vault backup: 2025-03-18 08:59:12

.obsidian/workspace.json

@@ -36,9 +36,9 @@
               "type": "pdf",
               "state": {
                 "file": "Concurrent Systems/slides/class 6.pdf",
-                "page": 1,
+                "page": 2,
                 "left": -24,
-                "top": 51,
+                "top": 282,
                 "zoom": 0.6448931116389548
               },
               "icon": "lucide-file-text",

Concurrent Systems/notes/6 - Atomicity.md

@@ -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.
+- $f$