\frametitle{Table}
If state $k$ with symbol $z$ writes $y$ to the tape
    and transitions into state $k'$ we get the following:
    \begin{columns}
    \begin{column}{0.52\textwidth}
    $$H_{kz} \mapsto [R_{k'*}R_{k'*}]^{ly}[H_{k'}]^{1-z}H_{k'}[L_{k'}L_{k'}]^{ry}$$
    $$L_{kz} \mapsto L_{k'}[L_{k'}L_{k'}L_{k'}]^r$$
    $$R_{kz} \mapsto R_{k'}[R_{k'}R_{k'}R_{k'}]^l$$
    $$H_{k}  \mapsto H_{k1}H_{k0}$$
    $$L_{k}  \mapsto L_{k1}L_{k0}$$
    $$R_{k}  \mapsto R_{k1}R_{k0}$$
    $$R_{k*} \mapsto R_kR_k$$
    \end{column}
    \begin{column}{0.48\textwidth}
        $$[H_{k1}]^zH_{k0}[L_{k1}L_{k0}]^{T_L}[R_{k1}R_{k0}]^{T_R}$$
        becomes
        $$H_{k'}[L_{k'}]^{(3r+1)T_L+2yr}[R_{k'}]^{(3l+1)T_R+2yl}$$
        becomes
        $$[H_{k1}]^{z'}H_{k0}[L_{k1}L_{k0}]^{\lfloor T_L/2\rfloor}[L_{k1}L_{k0}]^{2T_R}$$
        Where $z'$ is the next symbol
    \end{column}
\end{columns}