-
-
-
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.
$f^*(x_1,x_2,x_3) =
(x_2 \oplus x_3, \overline{x_1}\overline{x_3} + x_1\overline{x_2},
\overline{x_1}\overline{x_3} + x_1x_2)$
+
+
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*}
