vault backup: 2025-04-28 08:32:04

.obsidian/workspace.json

@@ -213,10 +213,10 @@
   },
   "active": "56150e6df7869900",
   "lastOpenFiles": [
-    "Concurrent Systems/slides/class 13.pdf",
-    "Concurrent Systems/notes/13 - Weak Bisimilarity.md",
-    "Concurrent Systems/slides/class 12.pdf",
     "Concurrent Systems/notes/12 - Calculus of communicating system.md",
+    "Concurrent Systems/notes/13 - Weak Bisimilarity.md",
+    "Concurrent Systems/slides/class 13.pdf",
+    "Concurrent Systems/slides/class 12.pdf",
     "Concurrent Systems/notes/12b - CCS cose varie.md",
     "Concurrent Systems/notes/11 - LTSs and Bisimulation.md",
     "HCIW/slides/HCI in the car.pdf",

Concurrent Systems/notes/13 - Weak Bisimilarity.md

@@ -7,4 +7,10 @@ The idea of the new equivalence is to ignore (some) τ’s:
 - a visible action must be replied to with the same action, possibly together with some internal actions
 - an internal action must be replied to by a (possibly empty) sequence of internal actions.
 
-$P \implies P'$ if and only if there exist $P_{0}, P_{1},\dots,P_{k}$ (for $k \geq 0$) such that $P=P_{0} \xrightarrow{\tau} P_{1} \xrightarrow{\tau}$
+We define the relation $\implies$ as:
+
+$P \implies P'$ if and only if there exist $P_{0}, P_{1},\dots,P_{k}$ (for $k \geq 0$) such that $P=P_{0} \xrightarrow{\tau} P_{1} \xrightarrow{\tau}\dots\xrightarrow{\tau}Pk=P'$
+
+relation $\xRightarrow{\hat{\alpha}}$:
+- if $\alpha=\tau$ then $\xRightarrow{\hat{\alpha}}\triangleq\implies$
+- otherwise $\xRightarrow{\hat{\alpha}}\triangleq\implies\xrightarr$