From a5af617983aac5c657a64b171efdd174585433db Mon Sep 17 00:00:00 2001 From: =?utf8?q?Jean-Fran=C3=A7ois=20Couchot?= Date: Mon, 16 Feb 2015 15:20:18 +0100 Subject: [PATCH] texte eps --- main.tex | 1 + preliminaries.tex | 11 +++++------ 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/main.tex b/main.tex index 67d9e93..6dbf3ef 100644 --- a/main.tex +++ b/main.tex @@ -6,6 +6,7 @@ \usepackage{ifthen} \usepackage{color} \usepackage{algorithm2e} +\usepackage{epstopdf} \usepackage[latin1]{inputenc} diff --git a/preliminaries.tex b/preliminaries.tex index 6d837a1..f90fdae 100644 --- a/preliminaries.tex +++ b/preliminaries.tex @@ -1,14 +1,11 @@ - - - In what follows, we consider the Boolean algebra on the set $\Bool=\{0,1\}$ with the classical operators of conjunction '.', of disjunction '+', of negation '$\overline{~}$', and of disjunctive union $\oplus$. Let $n$ be a positive integer. A {\emph{Boolean map} $f$ is -a function from the Boolean domain - to itself +a function from $\Bool^n$ +to itself such that $x=(x_1,\dots,x_n)$ maps to $f(x)=(f_1(x),\dots,f_n(x))$. Functions are iterated as follows. @@ -41,13 +38,15 @@ $f^*: \Bool^3 \rightarrow \Bool^3$ be defined by $f^*(x_1,x_2,x_3) = (x_2 \oplus x_3, \overline{x_1}\overline{x_3} + x_1\overline{x_2}, \overline{x_1}\overline{x_3} + x_1x_2)$ + + The iteration graph $\Gamma(f^*)$ of this function is given in Figure~\ref{fig:iteration:f*}. \vspace{-1em} \begin{figure}[ht] \begin{center} -\includegraphics[scale=0.5]{images/iter_f0b} +\includegraphics[scale=0.5]{images/iter_f0c.eps} \end{center} \vspace{-0.5em} \caption{Iteration Graph $\Gamma(f^*)$ of the function $f^*$}\label{fig:iteration:f*} -- 2.39.5