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diff --git a/assignment4/assignment4.tex b/assignment4/assignment4.tex new file mode 100644 index 0000000..e31b35e --- /dev/null +++ b/assignment4/assignment4.tex @@ -0,0 +1,51 @@ +\documentclass[10pt,a4paper]{article} + +\usepackage[margin=2cm]{geometry} + +\usepackage{minted} + +\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} +\usepackage{amsfonts} + +\usepackage{enumitem} +\setenumerate[1]{label=\alph*.} + +\parindent0pt + +\title{Operating Systems - assignment 4} +\author{Camil Staps\\\small{s4498062}} + +\begin{document} + +\maketitle +\thispagestyle{fancy} + +\section*{6.11} +%todo + +\section*{6.18} +\begin{enumerate} + \item If there are two types of philosophers, the fourth condition of deadlock (circular wait) is not fulfilled. Lefties and righties can never be in a chain waiting for resources. Therefore, deadlock cannot occur. + \item On a table with two philosophers, of which one is a lefty and one a righty, it is obvious to see that one philosopher will start eating and when he is done, the other one can grab the forks. No starvation occurs. + + If on a table with $k$ philosophers no starvation occurs, and we add another philosopher $p$, this new philosopher is placed between two philosophers who, at some point, will eat. Then at some point the first fork $p$ wants to take will be free, and also at some point the other fork $p$ needs will be free. Hence, $p$ will also eat. + + From the principle of induction it now follows that starvation cannot occur on a table with $n\ge2$ philosophers, as long as there is at least one lefty and one righty. +\end{enumerate} + +\end{document} + |