From 243dac16caa2788421d65a5d4ede2960fd5c8669 Mon Sep 17 00:00:00 2001
From: Marco Realacci <realacci.1938880@gamlab11.gamlab.sapienzaapps.it>
Date: Tue, 18 Mar 2025 15:24:57 +0100
Subject: [PATCH] vault backup: 2025-03-18 15:24:57

---
 .obsidian/workspace.json                  | 26 ++++++-----------------
 Concurrent Systems/notes/6 - Atomicity.md |  8 +++++--
 2 files changed, 13 insertions(+), 21 deletions(-)

diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json
index 0bbdbcb..ec77d71 100644
--- a/.obsidian/workspace.json
+++ b/.obsidian/workspace.json
@@ -6,7 +6,7 @@
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@@ -27,7 +27,7 @@
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@@ -35,11 +35,7 @@
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-                "page": 6,
-                "left": -23,
-                "top": 546,
-                "zoom": 0.6448931116389549
+                "file": "Concurrent Systems/slides/class 6.pdf"
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               "title": "class 6"
@@ -103,8 +99,7 @@
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@@ -178,8 +173,8 @@
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-              "title": "Source Control"
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@@ -209,14 +204,7 @@
       "canvas:Create new canvas": false,
       "daily-notes:Open today's daily note": false,
       "templates:Insert template": false,
-      "command-palette:Open command palette": false,
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diff --git a/Concurrent Systems/notes/6 - Atomicity.md b/Concurrent Systems/notes/6 - Atomicity.md
index 88a40ea..2677684 100644
--- a/Concurrent Systems/notes/6 - Atomicity.md	
+++ b/Concurrent Systems/notes/6 - Atomicity.md	
@@ -14,7 +14,7 @@ A history is **complete** if every inv is eventually followed by a corresponding
 ### Linearizability
 A complete history $\hat{H}$ is **linearizable** if there exists a sequential history $\hat{S}$ s.t.
 - $\forall X :\hat{S}|_{X} \in semantics(X)$
-- $\forall p:\hat{H}|_{p} = \hat{S}|p$
+- $\forall p:\hat{H}|_{p} = \hat{S}|_p$
 	- cannot swap actions performed by the same process
 - If $res[op] <_{H} inv[op']$, then $res[op] <_{S} inv[op']$
 	- can rearrange events only if they overlap
@@ -24,6 +24,7 @@ Given an history $\hat{K}$, we can define a binary relation on events $⟶_{K}$
 ![[Pasted image 20250318090733.png]]
 
 ![[Pasted image 20250318090909.png]]But there is another linearization possible! I can also push a before if I pull it before c!
+Of course I have to respect the semantics of a Queue (if I push "a" first, I have to pop "a" first because it's a fucking FIFO)
 
 #### Compositionality theorem
 $\hat{H}$ is linearizable if $\hat{H}|_{X}$ is linearizable, for all X in H
@@ -34,7 +35,10 @@ For all X, let $\hat{S}_{X}$ be a linearization of $\hat{H}_{X}$
 
 Let $\to$ denote $\to_{H} \cup \bigcup_{X \in H} \to _{X}$
 
-...
+We now show that $->$ is acyclic.
+
+
+
 > [!PDF|red] class 6, p.6>  we would have a cycle of length 
 > 
 > we would contraddict op2 ->x op3