From a662e0a5212c92b15c6e84cf2907c5463e60da20 Mon Sep 17 00:00:00 2001 From: Philip Kaludercic <philip.kaludercic@fau.de> Date: Sun, 7 Apr 2024 21:04:53 +0200 Subject: [PATCH] Clarify the definition of behavioural equivalence --- coalgebra.tex | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/coalgebra.tex b/coalgebra.tex index 0df45f0..0f57783 100644 --- a/coalgebra.tex +++ b/coalgebra.tex @@ -50,10 +50,11 @@ \begin{definition}\label{def:beheqiv} For a \de{endofunctor} \(F : \map{\Set}{\Set}\) and two \fca{} - \((C, c)\), \((D, d)\), are \emph{behaviourally equivalent} for - \(C \ni x \sim y \in D\) if - \[ \exists h, k \st (C, c) \xrightarrow{h} (E, e) \xleftarrow{k} (D, - d), \] for some \((E, e)\). + \((C, c)\), \((D, d)\) states \(x \in C\), \(y \in D\), are + \emph{behaviourally equivalent}, if for some + \((E, e)\), + \[ x \sim y \iff \exists h, k \st (C, c) \xrightarrow{h} (E, e) + \xleftarrow{k} (D, d). \] \end{definition} \begin{definition}\label{def:bisimulation} -- GitLab