From 8dd45af905df1927e3ff004c80a4a0b03ef2c18b Mon Sep 17 00:00:00 2001 From: Marco Realacci Date: Tue, 15 Apr 2025 09:05:18 +0200 Subject: [PATCH] vault backup: 2025-04-15 09:05:18 --- .obsidian/workspace.json | 2 +- Concurrent Systems/notes/13 - CCS cose varie.md | 11 +++++++++-- Pasted image 20250415090109.png | Bin 0 -> 10679 bytes 3 files changed, 10 insertions(+), 3 deletions(-) create mode 100644 Pasted image 20250415090109.png diff --git a/.obsidian/workspace.json b/.obsidian/workspace.json index a569f6b..3dbd8f9 100644 --- a/.obsidian/workspace.json +++ b/.obsidian/workspace.json @@ -230,6 +230,7 @@ "lastOpenFiles": [ "Concurrent Systems/slides/class 12.pdf", "Concurrent Systems/notes/13 - CCS cose varie.md", + "Pasted image 20250415090109.png", "Concurrent Systems/notes/12 - Calculus of communicating system.md", "Pasted image 20250415082906.png", "Concurrent Systems/notes/11 - LTSs and Bisimulation.md", @@ -242,7 +243,6 @@ "Concurrent Systems/notes/images/Pasted image 20250414152247.png", "Concurrent Systems/notes/images/Pasted image 20250414152234.png", "Concurrent Systems/notes/images/Pasted image 20250414152221.png", - "Concurrent Systems/notes/images/Pasted image 20250414104010.png", "HCIW/notes/3 - Beacons.md", "HCIW/slides/Zooming interfaces.pdf", "HCIW/slides/Gestural interaction.pdf", diff --git a/Concurrent Systems/notes/13 - CCS cose varie.md b/Concurrent Systems/notes/13 - CCS cose varie.md index 8ba455a..7d7e55c 100644 --- a/Concurrent Systems/notes/13 - CCS cose varie.md +++ b/Concurrent Systems/notes/13 - CCS cose varie.md @@ -47,5 +47,12 @@ Let's go! One of the main aims of an equivalence notion between processes is to make equational reasonings of the kind: “if P and Q are equivalent, then they can be interchangeably used in any execution context”. This feature on an equivalence makes it a *congruence* -Not all equivalences are necessarily congruences (even though most of them are -To properly define a congruence, we first need to define an execution context, and then what it means to run a process in a context. Intuitively: \ No newline at end of file +Not all equivalences are necessarily congruences (even though most of them are). +To properly define a congruence, we first need to define an execution context, and then what it means to run a process in a context. Intuitively: +![200](../../Pasted%20image%2020250415090109.png) + +where C is a context (i.e., a process with a hole ☐), P is a process, and $C[P]$ denotes filling the hole with P + +Example: $$if \space C = (☐ | Q) \textbackslash a, \space then \space C[P] = (P | Q) \textbackslash a$$ +The set C of CCS contexts is given by the following grammar: +$$C ::= ☐ \space | \space C|P \space | $$ \ No newline at end of file diff --git a/Pasted image 20250415090109.png b/Pasted image 20250415090109.png new file mode 100644 index 0000000000000000000000000000000000000000..805800e47d4cbef99a964c2e58e14fbed454c58d GIT binary patch literal 10679 zcmcgy_dA5d{GO0hNZjsy+e1t=GWoX);1!B!oUI z2X5q^>SjI!1b2J>UAHm>?lKV&un}meDjNpoZRL}vFoVx-F19YR;K4G@GsNEH-eh_S zaZjF9Q44icQ^%P9)!_T~K8MaUU9}PU9lB3yMEF<9)M_~*l9a5-m`+)_BaOO)nai#Q zznK?Wu+!cYTvHwl_V>3BK;X|DKhEUC;n?}>p^LWR3xx$zn*?$Kg1=;qWAp?B&r1m) zM9*Ds{a*})Cg+5+Gy`6gnApeh%mZV)ZwTe@6C1}#d_x9lOkCQwKaArt0YeD~$`Ac+ zbrju#+}xAu7BqC0RO42QaA4@Jb7@+;xJGKd{@a+*CQo3>EV^|m0^iAeKt-df!_Vj4 z=_%wX2tv~ufs2rpl7l1TudO)=1PRH?K#}A{x<;16nmk|BF*F(xI+~Fi7dRuZbMIXO zmRo(n_q%H)(Mx9BY19r18RR4$v;IaB#;fZD|Is|h-eSPz*lU3Uh%|aka*7x+e80ErA8i!7* z&y5PT@=}^O2x>G~nb$AmMd0Z39IM>Xf@I{n;5@I-$I;fEuZFdRm7Qo|?Gz9Ov8IBG#MZ#2&?UeF|}+)8Ky6iE5w}@cfT< z)gRIfcX%qS24(IZ_X&ATXPPq!8c=|x-z9LR>cf-F z=DBAEfMh<1ndM~vswN20Re7168tYHImk!`OzGiAXpY>$0+R=0xMa1coiF{ zGdYkmO8;GDP=)hLTR9}sCMlgChErFV%GB`k+Zj{a-guaR?YQ*)++u|8V&I9w-Gd%= z)Fdc05?WjQH-Ks=T1$Ol%gufS*1x0E=Rm!MZ>&7Nz4CQqiAC!RRT@Wsu}I6;zP|fv zBrk=JrXqsjO2#D*T=-*0kiOn^;W)2Y#N)-Q+k(%h`kRrAioF_oj;_tY+6-|}2o}}w z=;h|a+q6+Om{;-O`C8MQ?cv*0_a9}wN+BDiTZ8=jp5o@Et)R3Q0Yx)Huk`=mKRRdK z*)b$BrjC<0FAsue(tVtmd3#d&M+WRTi(=r{dVjVm40)4;3sOW$wl9!@44&~ZUIaE+ z>|Hh5y4G#nr570GhA8r#e6e#D%W$r->H2Yg|77Vs16oa^M3xN9m_=s40wPBaKEEH> zUv1Pah;-J`hhL}fTo}!NTaU({5u#S?ocKN*)9LXJd4=AML%ny0$#BPzt4X-!+O9s7 zBBC6G(nf=)BtLYh8p9&*(IiM=_$KJ44m6^wy^A7vXG2s!D5*}p2R5hKDBb*jeAO}; 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