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Marco Realacci 2025-04-30 17:13:22 +02:00
parent 0088cfa802
commit 9db7dc5841
2 changed files with 11 additions and 17 deletions
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21
.obsidian/workspace.json vendored
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@ -20,18 +20,6 @@
"icon": "lucide-file", "icon": "lucide-file",
"title": "13 - Weak Bisimilarity" "title": "13 - Weak Bisimilarity"
} }
},
{
"id": "4151b8cc103dc898",
"type": "leaf",
"state": {
"type": "pdf",
"state": {
"file": "Concurrent Systems/slides/class 13.pdf"
},
"icon": "lucide-file-text",
"title": "class 13"
}
} }
] ]
} }
@ -90,7 +78,8 @@
} }
], ],
"direction": "horizontal", "direction": "horizontal",
"width": 309.5 "width": 309.5,
"collapsed": true
}, },
"right": { "right": {
"id": "bc4b945ded1926e3", "id": "bc4b945ded1926e3",
@ -204,10 +193,10 @@
}, },
"active": "ec8d1a91f1f0cc7e", "active": "ec8d1a91f1f0cc7e",
"lastOpenFiles": [ "lastOpenFiles": [
"Concurrent Systems/notes/14.md",
"Concurrent Systems/notes/13 - Weak Bisimilarity.md",
"Concurrent Systems/notes/12b - CCS cose varie.md",
"Concurrent Systems/slides/class 13.pdf", "Concurrent Systems/slides/class 13.pdf",
"Concurrent Systems/notes/13 - Weak Bisimilarity.md",
"Concurrent Systems/notes/14.md",
"Concurrent Systems/notes/12b - CCS cose varie.md",
"Concurrent Systems/notes/12 - Calculus of communicating system.md", "Concurrent Systems/notes/12 - Calculus of communicating system.md",
"Concurrent Systems/notes/images/Pasted image 20250415082906.png", "Concurrent Systems/notes/images/Pasted image 20250415082906.png",
"Concurrent Systems/slides/class 14.pdf", "Concurrent Systems/slides/class 14.pdf",

5
Concurrent Systems/notes/13 - Weak Bisimilarity.md
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@ -110,3 +110,8 @@ Every component can be in three states:
- B (habilitated, with the possibility of being extracted or of habilitating the next component) - B (habilitated, with the possibility of being extracted or of habilitating the next component)
- C (extracted, waiting to externally communicate its value and start the process again): $$A_{i}=a_{i}.B_{i} \quad B_{i}=\tau.C_{i}+\bar{a}_{(i \space mod \space n)+1}.A_{i} \quad C_{i}=\bar{p}_{i}.B_{i}$$ - C (extracted, waiting to externally communicate its value and start the process again): $$A_{i}=a_{i}.B_{i} \quad B_{i}=\tau.C_{i}+\bar{a}_{(i \space mod \space n)+1}.A_{i} \quad C_{i}=\bar{p}_{i}.B_{i}$$
In pratica ogni volta o estrae di nuovo "se stesso" oppure "abilita" il componente successivo. In pratica ogni volta o estrae di nuovo "se stesso" oppure "abilita" il componente successivo.
Implementation: $$Impl \triangleq (B_{1}|A_{2}|\dots|An)$$
basically we need to have an initially habilitated process, which can be any (the first one in our case).
This will generate the LTS: