\documentclass{beamer}

% Theme selection
\usetheme{Madrid}

% Package imports
\usepackage{graphicx}
\usepackage{hyperref}

% Title and author information
\title[Short Title]{Your Presentation Title}
\author[Your Name]{Your Full Name}
\institute[Your Institution]{Your Institution \\ \href{mailto:your.email@example.com}{your.email@example.com}}
\date{\today}

\begin{document}

% Title slide
\begin{frame}
    \titlepage
\end{frame}

% Table of contents
\begin{frame}{Outline}
    \tableofcontents
\end{frame}

% Section 1
\section{Introduction}

\begin{frame}{Introduction to the Topic}
    \begin{itemize}
        \item Brief overview of the topic.
        \item Key importance of the topic.
        \item What you will cover in this presentation.
    \end{itemize}
\end{frame}

% Section 2
\section{Main Content}

\begin{frame}{First Key Point}
    \begin{block}{Definition}
        Define key terms or concepts here.
    \end{block}
    \begin{example}
        Provide an example or application here.
    \end{example}
\end{frame}

\begin{frame}{Second Key Point}
    \begin{columns}
        \column{0.5\textwidth}
        \begin{itemize}
            \item First item
            \item Second item
        \end{itemize}
        \column{0.5\textwidth}
        \includegraphics[width=\textwidth]{example-image} % Replace with your image
    \end{columns}
\end{frame}

% Section 3
\section{Conclusion}

\begin{frame}{Summary and Conclusion}
    \begin{itemize}
        \item Recap main points.
        \item Future directions or next steps.
        \item Thank the audience.
    \end{itemize}
\end{frame}

% Thank you slide
\begin{frame}{Thank You!}
    \centering
    Questions? \\
    \includegraphics[width=0.2\textwidth]{example-image-a} % Replace with your logo or image
\end{frame}

\begin{frame}[fragile]{Table}
    If state $k$ with symbol $0$ writes 0 to the tape, moves to the left
    and transitions into state $k'$ we get the following:
    \begin{columns}
    \begin{column}{0.45\textwidth}
    $$H_{k0} \mapsto H_{k'}H_{k'}$$
    $$L_{k0} \mapsto L_{k'}$$
    $$R_{k0} \mapsto R_{k'}R_{k'}R_{k'}R_{k'}$$
    $$H_{k}  \mapsto H_{k1}H_{k0}$$
    $$L_{k}  \mapsto L_{k1}L_{k0}$$
    $$R_{k}  \mapsto R_{k1}R_{k0}$$
    \end{column}
    \begin{column}{0.51\textwidth}
        $$H_{k0}[L_{k1}L_{k0}]^{T_L}[R_{k1}R_{k0}]^{T_R}$$
        becomes
        $$H_{k'}[L_{k'}]^{T_L}[R_{k'}]^{4T_R}$$
        becomes
        $$[H_{k'1}]^{z'}H_{k'0}[L_{k'1}L_{k'0}]^{\lfloor T_L/2\rfloor}[L_{k'1}L_{k'0}]^{2T_R}$$
        Where $z'$ is the next symbol
    \end{column}
\end{columns}
\end{frame}
\begin{frame}[fragile]{Table}
    If state $k$ with symbol $z$ writes $0$ to the tape, moves to the left
    and transitions into state $k'$ we get the following:
    \begin{columns}
    \begin{column}{0.48\textwidth}
    $$H_{kz} \mapsto [H_{k'}]^{1-z}H_{k'}$$
    $$L_{kz} \mapsto L_{k'}$$
    $$R_{kz} \mapsto R_{k'}R_{k'}R_{k'}R_{k'}$$
    $$H_{k}  \mapsto H_{k1}H_{k0}$$
    $$L_{k}  \mapsto L_{k1}L_{k0}$$
    $$R_{k}  \mapsto R_{k1}R_{k0}$$
    $$R_{k*} \mapsto R_kR_k$$
    \end{column}
    \begin{column}{0.48\textwidth}
        $$[H_{k1}]^zH_{k0}[L_{k1}L_{k0}]^{T_L}[R_{k1}R_{k0}]^{T_R}$$
        becomes
        $$H_{k'}[L_{k'}]^{T_L}[R_{k'}]^{4T_R}$$
        becomes
        $$[H_{k1}]^{z'}H_{k0}[L_{k1}L_{k0}]^{T_L'}[L_{k1}L_{k0}]^{T_R'}$$
        Where $z'$ is the next symbol
    \end{column}
\end{columns}
\end{frame}
\begin{frame}[fragile]{Table}
    If state $k$ with symbol $z$ writes $y$ to the tape, moves to the left
    and transitions into state $k'$ we get the following:
    \begin{columns}
    \begin{column}{0.48\textwidth}
    $$H_{kz} \mapsto [R_{k'*}R_{k'*}]^y[H_{k'}]^{1-z}H_{k'}$$
    $$L_{kz} \mapsto L_{k'}$$
    $$R_{kz} \mapsto R_{k'}R_{k'}R_{k'}R_{k'}$$
    $$H_{k}  \mapsto H_{k1}H_{k0}$$
    $$L_{k}  \mapsto L_{k1}L_{k0}$$
    $$R_{k}  \mapsto R_{k1}R_{k0}$$
    $$R_{k*} \mapsto R_kR_k$$
    \end{column}
    \begin{column}{0.48\textwidth}
        $$[H_{k1}]^zH_{k0}[L_{k1}L_{k0}]^{T_L}[R_{k1}R_{k0}]^{T_R}$$
        becomes
        $$[R_{k'*}R_{k'*}]^y H_{k'}[L_{k'}]^{T_L}[R_{k'}]^{4T_R}$$
        becomes
        $$H_{k'}[L_{k'}]^{T_L}[R_{k'}]^{4T_R+2y}$$
        becomes
        $$[H_{k1}]^{z'}H_{k0}[L_{k1}L_{k0}]^{T_L'}[L_{k1}L_{k0}]^{T_R'}$$
        Where $z'$ is the next symbol
    \end{column}
\end{columns}
\end{frame}

\begin{frame}[fragile]{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}
\end{frame}

\end{document}
    %hallo
