pouya/coalgebraic-simulation
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity

slides

Browse Source
This commit is contained in:
partowp
2026-07-25 17:19:22 +01:00
parent 4f9fc5a687
commit d94b780ca3
1 changed files with 10 additions and 10 deletions
Download Patch File Download Diff File Expand all files Collapse all files
ACV 2026/slides.tex
+10 -10
View File
@@ -165,7 +165,7 @@
The content of the talk:
\begin{itemize}
\item Intuitive introduction to coalgebra and (bi)simulation
\item Reviewing basic definitions of coalgebra and (bi)simulation
\item Reviewing definitions of coalgebra and (bi)simulation
\item Our motivation: To ease proving program equivalence
\item Relator-based notions
\item Span-based notions
@@ -177,14 +177,14 @@
When can we say that two systems \emph{behave the same}?
\end{alertblock}
\vspace{-0.4cm}
This question is everywhere, often silently assumed:\vspace{-0.4cm}
This question is everywhere, for example:\vspace{-0.4cm}
\begin{itemize}
\setlength{\itemsep}{6pt}
\item[\faServer] \textbf{Hardware redesign.} A chip redesigned for cheaper production must still compute exactly what the old one did.
\item[\faServer] \textbf{Hardware redesign.} A chip redesigned for a cheaper price must still compute exactly what the old one did.
\item[\faCode] \textbf{Software upgrades.} A bank replaces its backend --- from the customer's view (balances, transactions), nothing should change.
\end{itemize}
\vspace{0.2cm}
\begin{block}{The catch}
\begin{block}{The point}
``Behaving the same'' is intuitive, but making it \emph{precise} and \emph{checkable} is surprisingly subtle.
\end{block}
\end{frame}
@@ -453,8 +453,8 @@
-The method, applies a closure on the bisimilarity relation on $T$.\\
-Then one should prove that the result is a simulation.\\
-The closure preserves symmetry, and symmetric simulation is a bisimulation in traditional definitions.\\
-We have found out that it is not always the case.\\
-That is why we want to know when exactly a symmetric simulation is a bisimulation.
-We need to know how to generally derive bisimulation from simulation.\\
-And what is the impact of choosing specific notion of simulation (span-based, relation-based)?
\end{frame}
\begin{frame}{Relators and Simulations}
@@ -465,7 +465,7 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\column{.47\textwidth}
To define coalgebraic simulation, relators are invented.
Relators unify simulation and bisimulation.
\begin{alertblock}{Relator}
Assuming $F:\Set\to\Set$ is a functor, an $F$-relator a monotone map that sends a morphism of $\rel$ that is a relation $X\rto Y$ to a relation $FX\rto FY$.
\end{alertblock}
@@ -533,7 +533,7 @@
\begin{alertblock}{Symmetrization of a Relator}
Symmetrization of a relator $\relar$ is defined as:
\begin{gather*}
\hat{\relar}=\relar r\cap (\relar r^{-1})^{-1}
\hat{\relar}r=\relar r\cap (\relar r^{-1})^{-1}
\end{gather*}
\end{alertblock}
\begin{block}{Symmetric Relators}
@@ -658,8 +658,8 @@
\vspace{-0.1cm}
\begin{block}{}
\begin{itemize}
\item Although, not every sound and complete relator is a Barr relator.\\
\item We do not know when the symmetrizaion of a Barr relator is a Barr relator.
\item Although, not every sound and complete relator is a Barr relator!\\
\item We do not know when Clause 3 does not produce a Barr relator.
\end{itemize}
\end{block}
\end{frame}