texte eps

diff --git a/main.tex b/main.tex
index 67d9e936af243a66e45e676141d5702eacbde595..6dbf3ef2fedcfb5c4dbf19faf3a116e06ac241a9 100644 (file)
--- a/main.tex
+++ b/main.tex
@@ -6,6 +6,7 @@
 \usepackage{ifthen}
 \usepackage{color}
 \usepackage{algorithm2e}
 \usepackage{ifthen}
 \usepackage{color}
 \usepackage{algorithm2e}

+\usepackage{epstopdf}

 
 
 \usepackage[latin1]{inputenc}
 
 
 \usepackage[latin1]{inputenc}

diff --git a/preliminaries.tex b/preliminaries.tex
index 6d837a1114c7f639acc00992aac158d270a77e30..f90fdae53332d5bd734a41fcf8f4761913950f52 100644 (file)
--- 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 
 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. 
 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
 $f^*(x_1,x_2,x_3) = 
 (x_2 \oplus x_3, \overline{x_1}\overline{x_3} + x_1\overline{x_2},
 \overline{x_1}\overline{x_3} + x_1x_2)$
 $f^*(x_1,x_2,x_3) = 
 (x_2 \oplus x_3, \overline{x_1}\overline{x_3} + x_1\overline{x_2},
 \overline{x_1}\overline{x_3} + x_1x_2)$

+
+

 The iteration graph $\Gamma(f^*)$ of this function is given in 
 Figure~\ref{fig:iteration:f*}.
 
 \vspace{-1em}
 \begin{figure}[ht]
 \begin{center}
 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*}
 \end{center}
 \vspace{-0.5em}
 \caption{Iteration Graph $\Gamma(f^*)$ of the function $f^*$}\label{fig:iteration:f*}