X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/rairo15.git/blobdiff_plain/586298b57c6e1cec5566bbe692ac21c4c701fd51..a5af617983aac5c657a64b171efdd174585433db:/preliminaries.tex

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*}