78 lines
1.9 KiB
TeX
78 lines
1.9 KiB
TeX
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\documentclass[a4paper, 12pt]{article}
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\newcommand{\bold}{\textbf}
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\usepackage[english]{babel}
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\usepackage{amsmath}
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\usepackage{tikz}
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\usepackage{indentfirst}
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\begin{document}
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\newcommand{\q2}{\quad\quad}
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\title{\Large{\bold{Moontorio}}}
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\author{Matei Adriel}
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\date {}
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\maketitle
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\section{Describing a factory}
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A factory is made out of machines. A machine is either a provider, a belt or a consumer. Machines are connected by ports.
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\begin{figure}[h]
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\begin{equation}
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\begin{split}
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Machines\ A,\ B,\ C\ &::=\; belt\ p_i\ p_o \\
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&\quad|\quad provider\ p_1,\ p_2,\ ...\ p_n \\
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&\quad|\quad consumer\ p_1,\ p_2,\ ...\ p_n
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\end{split}
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\end{equation}
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\caption{Machines}
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\label{Machines}
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\end{figure}
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We can represent the factory as a directed graph, with the machines being the nodes and the ports being the edges:
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\vspace*{20pt}
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\begin{figure}[h]
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\centering
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\begin{tikzpicture}[shorten >=1pt, auto, node distance={50mm},
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main/.style = {draw, rectangle}]
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\node[main] (1) {$provider_1$};
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\node[main] (2) [right of=1] {$belt_1$};
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\node[main] (3) [right of=2] {$consumer_1$};
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\draw[->] (1) edge node{$p_1$} (2);
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\draw[->] (2) edge node{$p_2$} (3);
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\end{tikzpicture}
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\caption{Example of a simple factory}
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\label{SimpleFactory}
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\end{figure}
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\section{Constraints}
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The first step of the factory solving process is the constraint generation.
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We currently use 3 different types of constraints (Figure \ref{Constraints}).
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Let's take them one step at a time. The first two constrains (
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$p_k(t) <_{\Leftarrow} f(t)$ and $p_k(t) <_{\Rightarrow} f(t)$
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) are pretty similar, both limiting the flow through a port.
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\begin{figure}[ht]
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\begin{equation}
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\begin{split}
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Constraints\quad C_k\ &::=\; p_k(t) <_{\Leftarrow} f(t) \\
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&\quad|\quad p_k(t) <_{\Rightarrow} f(t) \\
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&\quad|\quad p_1(t) = p_2(f(t))
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\end{split}
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\end{equation}
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\caption{Constraints}
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\label{Constraints}
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\end{figure}
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\end{document}
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