\item \self
Find a \textit{symbolic encoding} for the set of initial states and the \textit{transition relation} of the following \emph{transition system} and
simplify your formulas. Use a binary encoding to encode the states, e.g.,
encode the state $s_2$ with the formula $v1 \wedge \neg v_0$.

\begin{center}
\vspace{-2em}
\begin{tikzpicture}[auto, node distance=3cm,shorten >=1pt,
thick,node/.style={circle,draw,minimum size=25pt}]
    \node[node] (s0) {$s_0$};
    \node[node] (s1) [right of=s0] {$s_1$};
    \node[node] (s2) [below of=s1] {$s_2$};
    \node[node] (s3) [below of=s0] {$s_3$};
    \path[<->] (s0) edge (s2);
    %\path[<->] (s0) edge (s2);
    %\path[<->] (s0) edge (s3);
    %\path[<->] (s1) edge (s2);
    \path[<->] (s1) edge (s3);
    %\path[<->] (s2) edge (s3);
    \path[->] (s0.120) edge[bend right=90, looseness=15, out=240, in=300] (s0.150);
    \path[->] (s1.30) edge[bend right=90, looseness=15, out=240, in=300] (s1.60);
    \path[->] (s2.30) edge[bend right=90, looseness=15, out=240, in=300] (s2.60);
    \path[->] (s3.120) edge[bend right=90, looseness=15, out=240, in=300] (s3.150);
\end{tikzpicture}
\end{center}