Added turing machine warm-up

Misc/Warm-Ups/turing.tex

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+\documentclass[
+	solutions,
+	hidewarning,
+	singlenumbering,
+	nopagenumber
+]{../../resources/ormc_handout}
+\usepackage{../../resources/macros}
+
+
+\title{Warm-Up: Turing Machine}
+\uptitler{\smallurl{}}
+\subtitle{Prepared by Mark on \today.}
+
+\begin{document}
+
+	\maketitle
+
+	Consider a turing machine that understands the following instructions:
+
+	\begin{itemize}[itemsep=2mm]
+		\item \texttt{>}: Move the tape right
+		\item \texttt{<}: Move the tape left
+		\item \texttt{+}: Increment the value in the current cell by 1. \par
+			If the resulting value exceeds 255, wrap to 0.
+		\item \texttt{-}: Decrement the value in the current cell by 1. \par
+			If the resulting value is smaller than 0, wrap to 255.
+		\item \texttt{[}: If the the value of the current cell is 0, jump to the matching \texttt{]}. \par
+			Otherwise, jump to the next instruction.
+		\item \texttt{]}: If the value of the current cell is 0, jump to the next instruction. \par
+			Otherwise, jump back to the matching \texttt{[}.
+	\end{itemize}
+
+
+	For example, the program \texttt{+>++>+++>++++>-} will set the first five cells to $[1, 2, 3, 4, 255]$. \par
+	All other cells will be zero, since they were not modified.
+
+	\problem{}
+	What does the snippet \texttt{[-]} do? \par
+	Is this different from \texttt{[+]}?
+
+	\vfill
+
+
+	\problem{}
+	What does \texttt{[->+<]} do?
+
+	\begin{solution}
+		Move the value of this cell into the next cell
+	\end{solution}
+
+	\vfill
+
+	\problem{}
+	Write a program that adds the value of the current cell to the next cell. \par
+	You do not need to preserve the value of the current cell.
+
+	\vfill
+	\pagebreak
+
+	\problem{}
+	What does \texttt{[>]} do?
+
+	\begin{solution}
+		Finds the first zero cell to the right
+	\end{solution}
+
+	\vfill
+
+	\problem{}
+	Write a program that copies the value of the current cell into the next cell,
+	preserving its initial value. \par
+	\hint{You may use as many "scratch" cells as you want.}
+
+	\vfill
+
+
+	\problem{}
+	Write a program that computes the product of the current cell and the next cell.
+
+
+	\vfill
+
+	\problem{Bonus}
+	Write a program that computes the square of the current cell. \par
+	(If your program starts at a cell with value \texttt{7}, it should end at a cell with value \texttt{49}.)
+
+	\vfill
+
+	\problem{Bonus}
+	What does \texttt{+[>[<-]<[->+<]>]>} do?
+
+	\begin{solution}
+		Finds the first non-zero cell to the right
+	\end{solution}
+
+\end{document}