Questionnaire-2024/equivalence_checking/theory_questions/4_3_tseitin_lect_sol.tex

Given are two combinational circuits $C_1$ and $C_2$.
First we translate $C_1$ and $C_2$ into their respective formula $\varphi_1$ and $\varphi_2$.
We need to check, whether $\varphi_1 \oplus \varphi_2$ is not satisfiable, i.e, \emph{$\varphi_1 \equiv \varphi_2$ if and only if $\varphi_1 \oplus \varphi_2$ is UNSAT}. Therefore, we perform the following steps.

\begin{itemize}
    \item We construct the formula $\varphi$:
    \begin{equation*}
    \begin{split}
    \varphi = \varphi_1 \oplus \varphi_2
    \end{split}
    \end{equation*}

    \item Next, the formula $\varphi$ has to be transformed into a CNF formula by using Tseitin encoding.

    \item Finally, the formula $CNF(\varphi)$ is given to a SAT solver. If the SAT solver determines that $CNF(\varphi)$ is unsatisfiable, then $\varphi_1 \equiv \varphi_2$.
    If the SAT solver determines that $CNF(\varphi)$ is satisfiable, then $\varphi_1 \not\equiv \varphi_2$.
\end{itemize}