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chapters/2_background.tex
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\chapter{Background}\label{ch:background}
%************************************************
\input{chapters/2_background_preamble}
\jip{TODO:\ Mention something about LCG.}
\noindent{}A goal shared between all programming languages is to provide a certain level
of abstraction: an assembly language allows you to abstract from the binary
instructions and memory positions; Low-level imperial languages, like FORTRAN,
were the first to allow you to abstract from the processor architecture of the
target machine; and nowadays writing a program requires little knowledge of the
actual workings of the hardware on which the program is executed.
Freuder states that the ``Holy Grail'' of programming languages would be where
the user merely states the problem, and the computer solves it and that
\gls{constraint-modelling} is one of the biggest steps towards this goal to
this day \autocite*{freuder-1997-holygrail}. Different from imperative (and
even other declarative) languages, in a \cml{} the modeller does not describe
how to solve the problem, but rather provides the problem requirements. You
could say that a constraint model actually describes the solution to the
problem.
In a constraint model, instead of specifying the manner in which we can find
the solution, we give a concise description of the problem. We describe what we
already know, the \parameters{}, what we wish to know, the \variables{}, and
the relationships that should exist between them, the \constraints{}.
This type of combinatorial problem is typically called a \gls{csp}. The goal of
a \gls{csp} is to find values for the \variables{} that satisfy the
\constraints{} or prove that no such assignment exists. Many \cmls\ also
support the modelling of \gls{cop}, where a \gls{csp} is augmented with a
\gls{objective} \(z\). In this case the goal is to find a solution that
satisfies all \constraints{} while minimising (or maximising) \(z\).
Although a constraint model does not contain any instructions on how to find a
suitable solution, these models can generally be given to a dedicated solving
program, or \solver{} for short, that can find a solution that fits the
requirements of the model.
\begin{example}%
\label{ex:back-knapsack}

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chapters/2_background_preamble.tex Normal file
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\noindent{}A goal shared between all programming languages is to provide a certain level
of abstraction: an assembly language allows you to abstract from the binary
instructions and memory positions; Low-level imperial languages, like FORTRAN,
were the first to allow you to abstract from the processor architecture of the
target machine; and nowadays writing a program requires little knowledge of the
actual workings of the hardware on which the program is executed.
Freuder states that the ``Holy Grail'' of programming languages would be where
the user merely states the problem, and the computer solves it and that
\gls{constraint-modelling} is one of the biggest steps towards this goal to
this day \autocite*{freuder-1997-holygrail}. Different from imperative (and
even other declarative) languages, in a \cml{} the modeller does not describe
how to solve the problem, but rather provides the problem requirements. You
could say that a constraint model actually describes the solution to the
problem.
In a constraint model, instead of specifying the manner in which we can find
the solution, we give a concise description of the problem. We describe what we
already know, the \parameters{}, what we wish to know, the \variables{}, and
the relationships that should exist between them, the \constraints{}.
This type of combinatorial problem is typically called a \gls{csp}. The goal of
a \gls{csp} is to find values for the \variables{} that satisfy the
\constraints{} or prove that no such assignment exists. Many \cmls\ also
support the modelling of \gls{cop}, where a \gls{csp} is augmented with a
\gls{objective} \(z\). In this case the goal is to find a solution that
satisfies all \constraints{} while minimising (or maximising) \(z\).
Although a constraint model does not contain any instructions on how to find a
suitable solution, these models can generally be given to a dedicated solving
program, or \solver{} for short, that can find a solution that fits the
requirements of the model.

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chapters/5_incremental.tex
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%************************************************
\chapter{Incremental Processing}\label{ch:incremental}
%************************************************