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improve foundations

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hannes.kuchelmeister
2020-02-24 16:47:45 +01:00
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25_Outline/sections/20_foundations.tex
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@@ -25,7 +25,7 @@ and \emph{constraints} $C$ that limit the solution space with
\subsection{Configuration State} \subsection{Configuration State}
A \emph{configuration} $S$ is defined by a tuple of variables (\autoref{eq:Foundations:ProductConfiguration:Variables}) and their corresponding domain value with We will define a \emph{configuration} $S$ as a tuple of variables (\autoref{eq:Foundations:ProductConfiguration:Variables}) and their corresponding domain value with
\begin{equation} \label{eq:Foundations:ProductConfiguration:ConfigurationState} \begin{equation} \label{eq:Foundations:ProductConfiguration:ConfigurationState}
S = \{ (v_i,\ d) \ |\ v_i \in V \ \land \ d \in \mathfrak{D}(i),\ i=1,\dotsc,m \}. S = \{ (v_i,\ d) \ |\ v_i \in V \ \land \ d \in \mathfrak{D}(i),\ i=1,\dotsc,m \}.
\end{equation} \end{equation}
@@ -44,6 +44,7 @@ with $solution\_space$ being the solution space of the corresponding constraint
\begin{equation} \label{eq:Foundations:ProductConfiguration:FinishedConfiguration} \begin{equation} \label{eq:Foundations:ProductConfiguration:FinishedConfiguration}
S_F \subset S,\ where \ \forall v_i \in V (\exists (v_i, d) \in S_F : d \in \mathfrak{D}(i)) \land is\_valid(S_F). S_F \subset S,\ where \ \forall v_i \in V (\exists (v_i, d) \in S_F : d \in \mathfrak{D}(i)) \land is\_valid(S_F).
\end{equation} \end{equation}
In practice a finished configuration of a product (or solution) is something that is ready to be produced. This means for example if we are configuring a car that the car could be produced in the specified way that is given by the finished configuration.
\section{Group-Based Product Configuration} \section{Group-Based Product Configuration}