clingo-dl.tex

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\begin{frame}{\clingodl}
  \begin{itemize}
  \item \structure{Idea} \ Extend \clingo\ with difference constraints over integers
  \item \structure{Features} \
    \begin{itemize}
    \item A difference constraint \
      \(
      {x-y}\leq c
      \)
      \par
      is represented as \
      \lstinline[mathescape]{&diff(x-y) <= c}
    \item Yields canonical witnessing integer assignments
    \end{itemize}
  \item \structure{References}   \ \cite{jakaosscscwa17a,karoscwa21a}
  \item \structure{Applications} \ \cite{abjoossctowa21a,hamunescwa23a,rascwachliso23a}
  \end{itemize}
\end{frame}
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\begin{frame}[fragile]{Example}
  \begin{onlyenv}<1>
\begin{lstlisting}[language=clingo,basicstyle=\small\ttfamily]
#const n=2.  #const m=1000.
task(1..n).  duration(T,200*T) :- task(T).

&dom { 1..m } = beg(T) :- task(T).
&dom { 1..m } = end(T) :- task(T).

&diff{end(T)-beg(T)} <= D :- duration(T,D).

&show { beg/1; end/1 }.
\end{lstlisting}
\end{onlyenv}
\begin{onlyenv}<2>
\begin{lstlisting}[language=clingo,basicstyle=\small\ttfamily]

task(1). task(2).   duration(1,200). duration(2,400).

&dom {1..1000} = beg(1).    &dom {1..1000} = beg(2).
&dom {1..1000} = end(1).    &dom {1..1000} = end(2).

&diff{end(1)-beg(1)}<=200.  &diff{end(2)-beg(2)}<=400.

&show{ beg/1; end/1 }.
\end{lstlisting}
\end{onlyenv}
\end{frame}
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