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zPW`tyr$G`O0@nVKbpfZ}vO3BG%AwtERN vWIfikQ)XS@&O4fxs};CV4S={Stealth[round]}] + \node[state, initial left, accepting] (q0p0) {$q_0, p_0$}; + \node[state] (q0p1) [right=of q0p0] {$q_0, p_1$}; + \node[state] (q0p2) [right=of q0p1] {$q_0, p_2$}; + \node[state, accepting] (q1p0) [below=of q0p0] {$q_1, p_0$}; + \node[state] (q1p1) [right=of q1p0] {$q_1, p_1$}; + \node[state] (q1p2) [right=of q1p1] {$q_1, p_2$}; + \node[state, accepting] (q2p0) [below=of q1p0] {$q_2, p_0$}; + \node[state, accepting] (q2p1) [right=of q2p0] {$q_2, p_1$}; + \node[state, accepting] (q2p2) [right=of q2p1] {$q_2, p_2$}; + + \path[->] + % Level 0 + (q0p0) edge node [above] {a} (q0p1) + (q0p1) edge node [above] {a} (q0p2) + (q0p2) edge [bend right] node [above] {a} (q0p0) + % Level 0 to level 1 + (q0p0) edge node [right] {b} (q1p0) + (q0p1) edge node [right] {b} (q1p1) + (q0p2) edge node [right] {b} (q1p2) + % Level 1 to level 2 + (q1p0) edge node [above] {a} (q2p1) + (q1p1) edge node [above] {a} (q2p2) + (q1p2) edge node [right, xshift=0.3cm] {a} (q2p0) + % Level 2 to level 1 + (q2p0) edge node [right] {b} (q1p0) + (q2p1) edge node [above left, yshift=0.1cm] {b} (q1p1) + (q2p2) edge node [right] {b} (q1p2) + % Level 2 + (q2p0) edge node [above] {a} (q2p1) + (q2p1) edge node [above] {a} (q2p2) + (q2p2) edge [bend left] node [below] {a} (q2p0) + % ──────────────────────────────────────────────────────────────────── + % Loops on level 1 + (q1p0) edge [loop left] node {b} () + (q1p1) edge [loop left] node {b} () + (q1p2) edge [loop left] node {b} (); + \end{tikzpicture} +\end{center} -\vspace{4cm} +\vspace{2.5cm} \begin{center} \begin{Large} - ``\textit{Sie können also alle C Programme in Kanonischer Ordnung aufzählen. Sollten Sie dies tun. Wahrscheinlich nicht. Was aber zählt ist, sie \textbf{können} es tun}'' + ``\textit{Sie können also alle C Programme in Kanonischer Ordnung aufzählen. Sollten Sie dies tun? Wahrscheinlich nicht. Was aber zählt ist, sie \textbf{können} es tun}'' \end{Large} \hspace{3cm} - Prof. Dr. Dennis Komm, 2025 \end{center} -\vspace{3cm} +\vspace{2cm} \begin{center} HS2025, ETHZ\\[0.2cm] \begin{Large} diff --git a/semester3/ti/main/parts/combinatorics.tex b/semester3/ti/main/parts/combinatorics.tex index 3b85d09..dfee9d0 100644 --- a/semester3/ti/main/parts/combinatorics.tex +++ b/semester3/ti/main/parts/combinatorics.tex @@ -2,6 +2,8 @@ \section{Combinatorics} \label{sec:combinatorics} \subsection{Introduction} +Please note: This section was not part of the book and is written in very simple terms (it is taken from a summary I wrote 4 years ago during Gymnasium) + Combinatorics was developed from the willingness of humans to gamble and the fact that everybody wanted to win as much money as possible. \subsection{Simple counting operations} diff --git a/semester3/ti/main/ti-summary.pdf b/semester3/ti/main/ti-summary.pdf index 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zq0%oiSTOx90u!M6Cg^la20399Bwd`Hv251=3$nt_ac?7zFE8U_{IssdTGeoa&~N`= g2VT)={Stealth[round]}] + \node[state, initial left, accepting] (q0p0) {$q_0, p_0$}; + \node[state] (q0p1) [right=of q0p0] {$q_0, p_1$}; + \node[state] (q0p2) [right=of q0p1] {$q_0, p_2$}; + \node[state, accepting] (q1p0) [below=of q0p0] {$q_1, p_0$}; + \node[state] (q1p1) [right=of q1p0] {$q_1, p_1$}; + \node[state] (q1p2) [right=of q1p1] {$q_1, p_2$}; + \node[state, accepting] (q2p0) [below=of q1p0] {$q_2, p_0$}; + \node[state, accepting] (q2p1) [right=of q2p0] {$q_2, p_1$}; + \node[state, accepting] (q2p2) [right=of q2p1] {$q_2, p_2$}; + \path[->] + % Level 0 + (q0p0) edge node [above] {a} (q0p1) + (q0p1) edge node [above] {a} (q0p2) + (q0p2) edge [bend right] node [above] {a} (q0p0) + % Level 0 to level 1 + (q0p0) edge node [right] {b} (q1p0) + (q0p1) edge node [right] {b} (q1p1) + (q0p2) edge node [right] {b} (q1p2) + % Level 1 to level 2 + (q1p0) edge node [above] {a} (q2p1) + (q1p1) edge node [above] {a} (q2p2) + (q1p2) edge node [right, xshift=0.3cm] {a} (q2p0) + % Level 2 to level 1 + (q2p0) edge node [right] {b} (q1p0) + (q2p1) edge node [above left, yshift=0.1cm] {b} (q1p1) + (q2p2) edge node [right] {b} (q1p2) + % Level 2 + (q2p0) edge node [above] {a} (q2p1) + (q2p1) edge node [above] {a} (q2p2) + (q2p2) edge [bend left] node [below] {a} (q2p0) + % ──────────────────────────────────────────────────────────────────── + % Loops on level 1 + (q1p0) edge [loop left] node {b} () + (q1p1) edge [loop left] node {b} () + (q1p2) edge [loop left] node {b} (); + \end{tikzpicture} +\end{center} -\vspace{4cm} +\vspace{3cm} \begin{center} \begin{Large} - ``\textit{Wenn Sie die Turing-Maschine als Touring-Maschine in der Prüfung schreiben, dann macht mich das sehr traurig. Ich seh das jeweils. Teilweise sind das sehr elaborierte Trolle, manchmal Leute die nie in die Vorlesungen kommen} (2025-10-14T08:51Z+02:00``) - - ``\textit{Sie können also alle C Programme in Kanonischer Ordnung aufzählen. Sollten Sie dies tun. Wahrscheinlich nicht. Was aber zählt ist, sie \textbf{können} es tun}'' + ``\textit{Sie können also alle C Programme in Kanonischer Ordnung aufzählen. Sollten Sie dies tun? Wahrscheinlich nicht. Was aber zählt ist, sie \textbf{können} es tun}'' \end{Large} \hspace{3cm} - Prof. Dr. Dennis Komm, 2025 @@ -52,7 +85,7 @@ \begin{scriptsize} \begin{itemize} \item \textit{Note: Definitions, Lemmas, etc are often 1:1 copies from the book or paraphrased (as I did not find an easier way of stating them)} - \item \textit{Note: In case I forgot to add the PDF page numbers, you can take the PDF page number is given by $P_{\text{PDF}} = P_{\text{Book}} + 15$} + \item \textit{Note: In case I forgot to add the PDF page numbers, the PDF page number is given by $P_{\text{PDF}} = P_{\text{Book}} + 15$} \end{itemize} \end{scriptsize}