\begin{itemize}
\item Boolean algebra on $\Bool=\{0,1\}$ with the classical operators: $.$, 
$+$, $\overline{~}$, disjunctive union $\oplus$
\item For $n \in \Nats^*$, a  {\emph{Boolean map}} $f$: 
a function 
\[
\Bool \rightarrow \Bool,  x=(x_1,\dots,x_n)\mapsto f(x)=(f_1(x),\dots,f_n(x))
\]
\item Dynamics: 
\begin{itemize}
\item $s = \left(s_t\right)_{t \in \mathds{N}}$: sequence of indices in $\llbracket 1;n \rrbracket$ called ``strategy''.
\item At the $t^{th}$ iteration: only the $s_{t}-$th component is
``iterated''
\[
\begin{array}{rcl}
x^{t+1}&=&F_f(s_t,x^t)\\
& \textrm{where}& \\
F_f& :&  \llbracket1;n\rrbracket\times \Bool^{n} \rightarrow \Bool^n\\
F_f(i,x)&=&(x_1,\dots,x_{i-1},f_i(x),x_{i+1},\dots,x_n)
\end{array}
\]
\end{itemize}
\end{itemize}

