From 6023957b481b55a9870111660f3bceb31dd3d31d Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Mon, 5 May 2025 08:57:04 +0200 Subject: [PATCH] vault backup: 2025-05-05 08:57:04 --- .obsidian/workspace.json | 1 + .../notes/15 - A formal language for LTSs.md | 7 +++++++ Pasted image 20250505085454.png | Bin 0 -> 152682 bytes 3 files changed, 8 insertions(+) create mode 100644 Pasted image 20250505085454.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index a9bcaab..b4e3dae 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -213,6 +213,7 @@ }, "active": "cdcc59f1bf6d4ae1", "lastOpenFiles": [ + "Pasted image 20250505085454.png", "Concurrent Systems/slides/class 15.pdf", "Concurrent Systems/notes/15 - A formal language for LTSs.md", "Pasted image 20250505084741.png", diff --git a/Concurrent Systems/notes/15 - A formal language for LTSs.md b/Concurrent Systems/notes/15 - A formal language for LTSs.md index be6cb9e..0056d32 100644 --- a/Concurrent Systems/notes/15 - A formal language for LTSs.md +++ b/Concurrent Systems/notes/15 - A formal language for LTSs.md @@ -25,3 +25,10 @@ Another very useful logical operator is "box": let us define $\lnot \lozenge a p ![](../../Pasted%20image%2020250505084741.png) From the last condition, we have that $P $\models \square a \phi$ if and only if $$\forall P': P \xrightarrow{a} P' \implies P' \models \phi$$ +EXAMPLE: Let us now consider formula ☐aFF +By definition, this happens only if, for every P’ resulting from P after action a, it holds P’ |= FF + +However, this can never happen, whatever P’ be; +hence, P |= ☐aFF holds true only if P cannot perform any action a + +![](../../Pasted%20image%2020250505085454.png) diff --git a/Pasted image 20250505085454.png b/Pasted image 20250505085454.png new file mode 100644 index 0000000000000000000000000000000000000000..09b6ce0159a0c81aeabb8edb287977ce2627cbeb GIT binary patch literal 152682 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