Questionnaire-2024/symbolic_encoding/0006_sol.tex

Using the variables $v_1$ and $v_0$, we can define the transition relation using the following formula:\\
\begin{center}
    $\lnot v_1 \land \lnot v_0 \land (\lnot v'_1 \land \lnot v'_0 \lor \lnot v'_1 \land v'_0 \lor v'_1 \land \lnot v'_0 \lor v'_1 \land v'_0) \ \lor$\\
    $\lnot v_1 \land v_0 \land (\lnot v'_1 \land v'_0 \lor v'_1 \land \lnot v'_0 \lor v'_1 \land v'_0) \ \lor$\\
    $v_1 \land \lnot v_0 \land (\lnot v'_1 \land \lnot v'_0 \lor \lnot v'_1 \land v'_0 \lor v'_1 \land v'_0) \ \lor$\\
    $v_1 \land v_0 \land (\lnot v'_1 \land \lnot v'_0 \lor \lnot v'_1 \land v'_0 \lor v'_1 \land \lnot v'_0 \lor v'_1 \land v'_0)$
\end{center}

We can further simplify the formula to:
\begin{center}
    $\lnot v_1 \land \lnot v_0 \lor$\\ 
    $\lnot v_1 \land v_0 \land (v'_0 \lor v'_1 \land \lnot v'_0) \ \lor$\\
    $v_1 \land \lnot v_0 \land (\lnot v'_1 \lor v'_1 \land v'_0) \ \lor$\\
    $v_1 \land v_0$
\end{center}