% LaTeX template for Models of Computation assessed coursework
% Most of the required packages are standard and should be provided by most TeX installations
% This file is released into the Public Domain
\documentclass[11pt,a4paper]{article}
\usepackage{fullpage}
\usepackage{rotating}
\usepackage{amsmath, amssymb, amsthm}
\usepackage{stmaryrd}
\usepackage{tikz}
\usepackage{verbatim}
\usepackage{url}
\usepackage{multicol}
\usepackage{xr-hyper}
\usetikzlibrary{automata}
\usetikzlibrary{arrows}
\usetikzlibrary{snakes}
\newcommand{\ang}[1]{\langle #1 \rangle}
\newcommand{\ra}{\rightarrow}
% Register Machines
\newcommand{\START}{\mathit{START}}
\newcommand{\HALT}{\mathit{HALT}}
\newcommand{\uinc}[2]{#1^+ \ra L_{#2}}
\newcommand{\udec}[3]{#1^- \ra L_{#2}, L_{#3}}
\newcommand{\iinc}[3]{L_{#1} & : \uinc{#2}{#3} \\}
\newcommand{\idec}[4]{L_{#1} & : \udec{#2}{#3}{#4} \\}
\newcommand{\ihalt}[1]{L_{#1} & : \HALT \\}
\newcommand{\code}[1]{\ulcorner{#1}\urcorner}
\newcommand{\ppair}[1]{\langle\hspace{-0.6ex}\langle #1 \rangle\hspace{-0.6ex}\rangle}
\newcommand{\pair}[1]{\ang{#1}}
\begin{document}
\title{Models of Computation Assessed Coursework II}
\author{A. Student}
\maketitle
This document is a skeleton which provides macros to help typeset your solution to the coursework.
Register machine rules can be typeset like this:
\[ \begin{array}{r@{\ }l}
\idec{0}{R_1}{3}{5}
\idec{1}{R_1}{4}{2}
\ihalt{2}
\idec{3}{R_1}{1}{2}
\iinc{4}{R_0}{0}
\ihalt{5}
\end{array} \]
Pairs and encodings:
\begin{gather*}
\ppair{1,2} \\
\pair{3,4} \\
\code{[1,2,3,4]} = \ppair{1,\ppair{2,\ppair{3,\ppair{4,0}}}} \\
\code{\uinc{R_1}{2}}
\end{gather*}
Graphing a register machine:
\begin{center}
\begin{tikzpicture}[baseline=(current bounding box.center),node distance=1.5cm,thick]
\node (S) {$\START$};
\node (L0) [right of=S] {$R_n^-$};
\node (L1) [right of=L0] {$\HALT$};
\node (L2) [below of=L0] {$R_m^+$};
\path[->] (S) edge (L0)
(L0) edge (L1) edge[bend right,->>] (L2)
(L2) edge[bend right] (L1);
\end{tikzpicture}
\end{center}
Other useful notation:
\begin{gather*}
\mathbb{N} \\
n_\phi
\end{gather*}
\end{document}
