vault backup: 2025-03-10 09:40:11
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a21e507d65
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2 changed files with 14 additions and 6 deletions
9
.obsidian/workspace.json
vendored
9
.obsidian/workspace.json
vendored
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@ -34,9 +34,9 @@
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"type": "pdf",
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"state": {
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"file": "Concurrent Systems/slides/class 3.pdf",
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"page": 7,
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"page": 9,
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"left": -26,
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"top": 213,
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"top": 276,
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"zoom": 0.57541567695962
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},
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"icon": "lucide-file-text",
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@ -218,10 +218,10 @@
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},
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"active": "6edd4157a160e462",
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"lastOpenFiles": [
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"Concurrent Systems/slides/class 3.pdf",
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"Concurrent Systems/notes/3.md",
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"Concurrent Systems/notes/1 - CS Basics.md",
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"Concurrent Systems/notes/1 - CS Basics2.md",
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"Concurrent Systems/notes/3.md",
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"Concurrent Systems/slides/class 3.pdf",
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"Concurrent Systems/notes/2b - Round Robin algorithm.md",
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"Concurrent Systems/notes/2 - Fast mutex by Lamport.md",
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"Concurrent Systems/notes/1b - Peterson algorithm.md",
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@ -263,7 +263,6 @@
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"Biometric Systems/frequently asked questions/BS_questions.txt.md",
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"Biometric Systems/notes/9. Ear recognition.md",
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"Biometric Systems/notes/13. Multi biometric.md",
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"Biometric Systems/notes/4. Face detection.md",
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"Senza nome.canvas"
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]
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}
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@ -154,4 +154,13 @@ Without it, if two process $i$ and $j$ sets MY_TURN at the same time, then $i$ g
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*Proof:*
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- let t be the value of `MY_TURN[i]` after $p_{i}$ exits the doorway (after flag <- down)
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- when $p_j$ computes its ticket, it reads $t$ from `MY_TURN[i]`, it reads t from MY_TURNpi
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- when $p_j$ computes its ticket, it reads $t$ from `MY_TURN[i]`, it reads t from `MY_TURN[i]` (no write overlapping with this read)
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- Hence, `MY_TURN[j]` is at least $t+1$.
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**Lemma 2:** Let $p_i$ be in the CS and $p_j$ is in the doorway or in the bakery; then, $$⟨MY\_TURN[i] , i⟩ < ⟨MY\_TURN[j] , j⟩$$*Proof:*
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If $p_i$ is in the CS, it has terminated its first wait for $j$
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let's consider the read of `FLAG[j]` done by $p_i$ that terminates such wait
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W.r.t. the execution of $p_j$, it can be that
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- this read overlaps with `FLAG[j] <- up` by Lemma 1, `MY_TURN[i] < MY_TURN[j]` and ok
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- this read is contained within the computation of `MY_TURN[j]`, but it's not possible, since `MY_TURN` is computed with the
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