marcorealacci/master-degree-notes
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

vault backup: 2025-04-15 16:15:01

Browse source
This commit is contained in:
Marco Realacci 2025-04-15 16:15:01 +02:00
parent 592fc55cff
commit f8a2d4a2d6
2 changed files with 5 additions and 5 deletions
Download patch file Download diff file Expand all files Collapse all files

6
.obsidian/workspace.json vendored
View file

@ -41,12 +41,12 @@
"state": { "state": {
"type": "markdown", "type": "markdown",
"state": { "state": {
"file": "Concurrent Systems/notes/12 - Calculus of communicating system.md", "file": "Concurrent Systems/notes/12b - CCS cose varie.md",
"mode": "source", "mode": "source",
"source": false "source": false
}, },
"icon": "lucide-file", "icon": "lucide-file",
"title": "12 - Calculus of communicating system" "title": "12b - CCS cose varie"
} }
} }
], ],
@ -221,8 +221,8 @@
}, },
"active": "a222ab88db5cfdd0", "active": "a222ab88db5cfdd0",
"lastOpenFiles": [ "lastOpenFiles": [
"Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
"Concurrent Systems/notes/12 - Calculus of communicating system.md", "Concurrent Systems/notes/12 - Calculus of communicating system.md",
"Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
"Concurrent Systems/notes/10 - Implementing Consensus.md", "Concurrent Systems/notes/10 - Implementing Consensus.md",
"Concurrent Systems/notes/12b - CCS cose varie.md", "Concurrent Systems/notes/12b - CCS cose varie.md",
"Concurrent Systems/slides/class 12.pdf", "Concurrent Systems/slides/class 12.pdf",

4
Concurrent Systems/notes/12b - CCS cose varie.md
View file

@ -2,10 +2,10 @@ An n-ary semaphore S(n)(p,v) is a process used to ensure that there are no more
The specification of a unary semaphore is the following: The specification of a unary semaphore is the following:
$$S^{(1)} \triangleq p \cdot S_{1}^{(1)}$$ $$S^{(1)} \triangleq p \cdot S_{1}^{(1)}$$
$$S_{1}^{(1)} \triangleq p \cdot S_{1}^{(1)}$$ $$S_{1}^{(1)} \triangleq p \cdot S_{}^{(1)}$$
The specification of a binary semaphore is the following: The specification of a binary semaphore is the following:
$$S_{}^{(2)} \triangleq p \cdot S_{1}^{(2)}$$ $$S_{}^{(2)} \triangleq p \cdot S_{1}^{(2)}$$
$$S_{1}^{(2)} \triangleq p \cdot S_{1}^{(2)}+v\cdot S^{(2)}$$ $$S_{1}^{(2)} \triangleq p \cdot S_{2}^{(2)}+v\cdot S^{(2)}$$
$$S_{2}^{(2)} \triangleq v \cdot S_{1}^{(2)}$$ $$S_{2}^{(2)} \triangleq v \cdot S_{1}^{(2)}$$
If we consider S(2) as the specification of the expected behavior of a binary semaphore and S(1) | S(1) as its concrete implementation, we can show that $$S^{(1)}|S^{(1)} \space \textasciitilde \space S^{2}$$ If we consider S(2) as the specification of the expected behavior of a binary semaphore and S(1) | S(1) as its concrete implementation, we can show that $$S^{(1)}|S^{(1)} \space \textasciitilde \space S^{2}$$