27 lines
No EOL
1 KiB
TeX
27 lines
No EOL
1 KiB
TeX
\documentclass[99-notes-packed.tex]{subfiles}
|
|
|
|
\begin{document}
|
|
|
|
\begin{background}[lattice]
|
|
A \textbf{lattice} describes a real coordinate space $\mathbb{R}^n$ that satisfies:
|
|
\begin{itemize}
|
|
\item {
|
|
Addition / subtraction between two points always produce another point in lattice -- i.e., closed under addition / subtraction.
|
|
}
|
|
\item {
|
|
Lattice points are separated by bounded distances in some range $(0, \mathrm{max}]$.
|
|
}
|
|
\end{itemize}
|
|
\end{background}
|
|
|
|
Define a lattice over which \textit{semantic equivalence relations} for spec. and impl. verification is defined.
|
|
|
|
\begin{definition}[discrimination measure]
|
|
One equivalence relation $\equiv$ is \textbf{finer} / \textbf{more discriminating} than another $\sim$ if each $\equiv$-eq. class is a subset of a $\sim$-eq. class. In other words,
|
|
\begin{align*}
|
|
\ &p \equiv q \implies p \sim q \\
|
|
\iff\ &\equiv\ \mathrm{finer\ than}\ \sim
|
|
\end{align*}
|
|
\end{definition}
|
|
|
|
\end{document} |