vault backup: 2025-03-25 18:07:22

.obsidian/workspace.json

@@ -14,12 +14,12 @@
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               },
               "icon": "lucide-file",
-              "title": "1b - Peterson algorithm"
+              "title": "8 - Enhancing Liveness Properties"
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@@ -98,7 +98,8 @@
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+    "width": 307.5,
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@@ -212,12 +213,12 @@
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+    "Concurrent Systems/slides/class 8.pdf",
+    "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",
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     "Concurrent Systems/notes/1b - Peterson algorithm.md",
     "Concurrent Systems/notes/2b - Round Robin algorithm.md",
     "Concurrent Systems/notes/2 - Fast mutex by Lamport.md",
-    "Concurrent Systems/notes/8 - Enhancing Liveness Properties.md",
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Concurrent Systems/notes/8 - Enhancing Liveness Properties.md

@@ -115,3 +115,12 @@ stop_help(i) :=
 
 ##### Theorem:
 the contention manager just seen transforms an obstruction-free implementation into a wait-free enriched implementation.
+
+*Proof:*
+By contradiction, $\exists$ an invocation of a correct $p_i$ that never terminates.
+Let $ti$ be its timestamp.
+- choose the minimum of such ⟨ti,i⟩
+
+By constraint of weak_ts(), the set of invocations smaller than ⟨ti,i⟩ (call it I) is finite
+- for every invocation ∈ I from a process $p_j$ that crashed during its execution
+	- $p_i$ will eventually and forever suspect $p_j$ (i.e. j ∈ `suspected_i`)