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author | Camil Staps | 2015-08-30 21:47:43 +0200 |
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committer | Camil Staps | 2015-08-30 21:47:43 +0200 |
commit | 27914510eb1cad054e54578d301e51a3e85e670e (patch) | |
tree | f7651bd9b090879d2dd51aa87805e72bc577e85b | |
parent | Initial commit (diff) |
Ex 9.1 start
-rw-r--r-- | ex9-1.tex | 13 | ||||
-rw-r--r-- | exercises.tex | 39 |
2 files changed, 52 insertions, 0 deletions
diff --git a/ex9-1.tex b/ex9-1.tex new file mode 100644 index 0000000..c416fdb --- /dev/null +++ b/ex9-1.tex @@ -0,0 +1,13 @@ +\begin{solution}{1} + \begin{enumerate} + \item \begin{align*} + & q_0BaabcaB \\\vdash& Bq_1aabcaB \\\vdash& Baq_1abcaB \\\vdash& Baaq_1bcaB \\\vdash& Baacq_1caB \\\vdash& Baaccq_1aB \\\vdash& Baaccaq_1B \\\vdash& Baaccq_2aB \\\vdash& Baacq_2ccB \\\vdash& Baaq_2cbcB \\\vdash& Baq_2abbcB \\\vdash& Bq_2acbbcB \\\vdash& q_2BccbbcB. + \end{align*} + \item \begin{align*} + & q_0BbcbcB \\\vdash& Bq_1bcbcB \\\vdash& Bcq_1cbcB \\\vdash& Bccq_1bcB \\\vdash& Bcccq_1cB \\\vdash& Bccccq_1B \\\vdash& Bcccq_2cB \\\vdash& Bccq_2cbB \\\vdash& Bcq_2cbbB \\\vdash& Bq_2cbbbB \\\vdash& q_2BbbbbB. + \end{align*} + \item Todo %todo + \item All $b$s in the input string are replaced by $c$s. All $c$s are replace by $b$s. All $b$s are left intact. The machine terminates in a normal fashion with the tape head on position $0$. + \end{enumerate} +\end{solution} + diff --git a/exercises.tex b/exercises.tex new file mode 100644 index 0000000..ce25ccd --- /dev/null +++ b/exercises.tex @@ -0,0 +1,39 @@ +\documentclass[10pt,a4paper,twocolumn]{article} + +\usepackage[margin=2cm]{geometry} +\usepackage{fourier} + +\usepackage{enumitem} +\setenumerate[1]{label=\alph*)} + +% textcomp package is not available everywhere, and we only need the Copyright symbol +% taken from http://tex.stackexchange.com/a/1677/23992 +\DeclareTextCommandDefault{\textregistered}{\textcircled{\check@mathfonts\fontsize\sf@size\z@\math@fontsfalse\selectfont R}} + +\usepackage{fancyhdr} +\renewcommand{\headrulewidth}{0pt} +\renewcommand{\footrulewidth}{0pt} +\fancyhead{} +\fancyfoot[C]{Copyright \textcopyright 2015 Camil Staps} +\pagestyle{fancy} + +\usepackage{amsmath} + +% Solution environment +\newenvironment{solution}[1]{\medskip\noindent{\textbf{Exercise \thesection.#1}\rm\par}{\medskip}} + +\parindent0pt + +\title{Solutions to selected exercises from Thomas Sudkamp, \textit{Languages and Machines} (second edition)} +\author{Camil Staps} + +\begin{document} + +\maketitle + +\setcounter{section}{8} +\section{Turing machines} +\input{ex9-1.tex} + +\end{document} + |