From 3e2dc34e618d585e4503a5b8db8b599f4f1be920 Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 15 Apr 2025 08:30:18 +0200 Subject: [PATCH] vault backup: 2025-04-15 08:30:18 --- .obsidian/workspace.json | 6 +++--- Concurrent Systems/notes/13 -.md | 6 ++++++ Pasted image 20250415082906.png | Bin 0 -> 56102 bytes 3 files changed, 9 insertions(+), 3 deletions(-) create mode 100644 Pasted image 20250415082906.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index 5c30757..836497b 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -226,10 +226,11 @@ "companion:Toggle completion": false } }, - "active": "46d9dfa1750fc4db", + "active": "9d3f25b0eb9b478f", "lastOpenFiles": [ - "Concurrent Systems/notes/13 -.md", "Concurrent Systems/slides/class 12.pdf", + "Concurrent Systems/notes/13 -.md", + "Pasted image 20250415082906.png", "Concurrent Systems/notes/12 - Calculus of communicating system.md", "Concurrent Systems/notes/11 - LTSs and Bisimulation.md", "Concurrent Systems/notes/images/Pasted image 20250414164549.png", @@ -242,7 +243,6 @@ "Concurrent Systems/notes/images/Pasted image 20250414152234.png", "Concurrent Systems/notes/images/Pasted image 20250414152221.png", "Concurrent Systems/notes/images/Pasted image 20250414104010.png", - "Concurrent Systems/notes/images/Pasted image 20250414103800.png", "HCIW/notes/3 - Beacons.md", "HCIW/slides/Zooming interfaces.pdf", "HCIW/slides/Gestural interaction.pdf", diff --git a/Concurrent Systems/notes/13 -.md b/Concurrent Systems/notes/13 -.md index a60a1d1..3f11c4c 100644 --- a/Concurrent Systems/notes/13 -.md +++ b/Concurrent Systems/notes/13 -.md @@ -7,3 +7,9 @@ The specification of a binary semaphore is the following: $$S_{}^{(2)} \triangleq p \cdot S_{1}^{(2)}$$ $$S_{1}^{(2)} \triangleq p \cdot S_{1}^{(2)}+v\cdot S^{(2)}$$ $$S_{2}^{(2)} \triangleq v \cdot S_{1}^{(2)}$$ + +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 $$S^{(1)}|S^{(1)} \space \textasciitilde \space S^{2}$$ +This means that the implementation and the specification do coincide. To show this equivalence, it suffices to show that following relation is a bisimulation: +![](../../Pasted%20image%2020250415082906.png) + +## Congruence diff --git a/Pasted image 20250415082906.png b/Pasted image 20250415082906.png new file mode 100644 index 0000000000000000000000000000000000000000..eb41a529a28248485a2a4fc582f87672419b45df GIT binary patch literal 56102 zcmX_{b95)c67ORt8#^0pY}>YN+qP{xzie#Vwr$(C-roD(eSZv2PfeYk)7_`%TlJ|3 zd08=d7;G3IARu@NabZOuAW(sS_wi65|IPwvFB$(X(DvdQPC!5iga0{zQ>YMdfPe^q zB!mT&-Lo&dAf2^Oe0D#!c&}t{z=JY?>B)r&`H`s!C|o6yg*OsSv|{nNd}W>Pb?=`$ zJB@cXTGoiYT%8hSTv7N&H2B;`QmbSmP`yAUYJr3aJ@NJZ&$@Qrr}5&E`2%Hwp%OE9 zI5@>1v)i0*eteI9zNiKtxXBgrg(HwjB$LVSgn?_G;gkP=gS);Yr}qDSq>w+DBqk9? z^*>wpd-5~;|Ge|x2D#rPc-8;UiNgL^LE%8k|D14pBs;hM*ZY4g$$mLE+5P>mCAX_R z^@IW{KLeCN0wl-f1MWZ_^V9)iG-46naRb7H1Gfk;SO~*opS39W%ssV;6DDjP5o+&j ziEEr3V-c3>fBVcEdcwhp2Q9Xs>o;x8X5}o&0Q9RifDwxm<#(2uhVpqW4heg7O7qSP 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