diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 643eb4c..f0739e3 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -34,6 +34,22 @@ "icon": "lucide-file", "title": "3b - Aravind's algorithm and improvements" } + }, + { + "id": "b51891c564d42ef8", + "type": "leaf", + "state": { + "type": "pdf", + "state": { + "file": "Concurrent Systems/slides/class 3.pdf", + "page": 17, + "left": -16, + "top": 596, + "zoom": 0.9236935866983375 + }, + "icon": "lucide-file-text", + "title": "class 3" + } } ], "currentTab": 1 @@ -210,12 +226,12 @@ }, "active": "dd6c003f9d17b0e9", "lastOpenFiles": [ - "Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md", + "Concurrent Systems/slides/class 3.pdf", "Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md", + "Concurrent Systems/notes/3a - Hardware primitives & Lamport Bakery algorithm.md", "Concurrent Systems/notes/1 - CS Basics.md", "Concurrent Systems/notes/2b - Round Robin algorithm.md", "Concurrent Systems/notes/2 - Fast mutex by Lamport.md", - "Concurrent Systems/slides/class 3.pdf", "Pasted image 20250310172134.png", "Pasted image 20250310103703.png", "Concurrent Systems/notes/1 - CS Basics2.md", diff --git a/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md b/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md index c09f8cf..601d10a 100644 --- a/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md +++ b/Concurrent Systems/notes/3b - Aravind's algorithm and improvements.md @@ -91,3 +91,8 @@ lock(i) := until foreach j != i, STAGE[j] = 0 ``` +- $p_n$ invokes lock alone, completes its CS and its new DATE is n + +**Lemma 1:** DATE's bounds are $[0, n]$ +*Proof:* +For the upper bound, it's trivial: DATE is either decreased or set to $n$. \ No newline at end of file