From d98fdef7847539b5042e7790625c4ea6283bc276 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sun, 26 Oct 2025 08:23:52 +0100 Subject: [PATCH] [TI] Fix a few typos --- .../02_proofs-of-nonexistance.tex | 9 +++++++-- .../02_finite-automata/03_non-determinism.tex | 9 +++++++-- .../01_multi-band-church-thesis.tex | 2 +- semester3/ti/ti-summary.pdf | Bin 958838 -> 959023 bytes 4 files changed, 15 insertions(+), 5 deletions(-) diff --git a/semester3/ti/parts/02_finite-automata/02_proofs-of-nonexistance.tex b/semester3/ti/parts/02_finite-automata/02_proofs-of-nonexistance.tex index 506cb40..11db675 100644 --- a/semester3/ti/parts/02_finite-automata/02_proofs-of-nonexistance.tex +++ b/semester3/ti/parts/02_finite-automata/02_proofs-of-nonexistance.tex @@ -88,10 +88,15 @@ da $yx^0z = yz = 0^{n_0 - m} 1^{n_0} \notin L$ ($0^{n_0}1^{n_0}$ ist sogar das e \inlineintuition Woher kommt $0^{n_0 - m + km}$? Das Ganze wird mit Klammern bedeutend offensichtlicher: $0^{(n_0 - m) + (km)}$. Also ist der Ursprung der Koeffizienten auch klar, und sie kommen von $|y| = n_0 - m$ und $|x^k| = km$. -Die Addition im Exponent kommt dann deshalb zustande, da dies ja nicht ein exponent ist, sondern die Anzahl der Repetitionen. +Die Addition im Exponent kommt dann deshalb zustande, da dies ja nicht ein Exponent ist, sondern die Anzahl der Repetitionen. \numberingOn + +\vspace{0.3cm} +\hrule +\vspace{0.2cm} + \fhlc{Cyan}{Kolmogorov-Komplexität basiert} \begin{theorem}[]{Kolmogorov-Komplexität regulärer Sprachen} @@ -128,7 +133,7 @@ $y_1$ (das erste Wort der Sprache $L_x$) ist dann $y_1 = 0^{(m + 1)^2 \cdot 2(m Wir können dann mit der Länge des Wortes $|y_1|$ und dem Theorem 3.1 argumentieren, dass wir einen Widerspruch erreichen und so also die Sprache nichtregulär ist. -Dazu sagen wir, dass für jedes $m \in \N$ ein $c$ existiert, so dass $K(y_1) \leq \ceil{\log_2(1 + 1)} + c = 1 + c$. +Dazu sagen wir, dass für jedes $m \in \N$ eine Konstante $c$ existiert, so dass $K(y_1) \leq \ceil{\log_2(1 + 1)} + c = 1 + c$. Da unser Wort $y_1$ unendlich lang werden kann, gibt es unendlich viele solcher Wörter. Dies widerspricht jedoch dem Fakt, dass es nur endlich viele Programme mit Kolmogorov-Komplexität $\leq 1 + c$ gibt. diff --git a/semester3/ti/parts/02_finite-automata/03_non-determinism.tex b/semester3/ti/parts/02_finite-automata/03_non-determinism.tex index 25247a0..eb101f2 100644 --- a/semester3/ti/parts/02_finite-automata/03_non-determinism.tex +++ b/semester3/ti/parts/02_finite-automata/03_non-determinism.tex @@ -105,8 +105,13 @@ Man kann beweisen (siehe Seiten 83 und 84 mit Abbildung 3.19 im Buch (= Seiten 9 % FIXME: Verify with TA that this is correct too % Else: Note an example from the worked example, TA's approach from the slides or from the book on P100 (PDF) -\fhlc{ForestGreen}{Worked Example} Zeige, das jeder endliche Automat, -der die Sprache $L = \{ w \in \{ a , b \}^* \divides w \text{ enthält Teilwort $ab$ gleich oft wie das Teilwort $ba$ enthält} \}$ +\fhlc{ForestGreen}{Worked Example} Zeige, das jeder endliche Automat, der die Sprache +\rmvspace +\begin{align*} + L = \{ w \in \{ a , b \}^* \divides w \text{ enthält Teilwort $ab$ gleich oft wie das Teilwort $ba$ enthält} \} +\end{align*} + +\drmvspace mindestens $n := 5$ Zustände haben muss. \begin{table}[h!] diff --git a/semester3/ti/parts/03_turing_machines/01_multi-band-church-thesis.tex b/semester3/ti/parts/03_turing_machines/01_multi-band-church-thesis.tex index 710c183..47348d9 100644 --- a/semester3/ti/parts/03_turing_machines/01_multi-band-church-thesis.tex +++ b/semester3/ti/parts/03_turing_machines/01_multi-band-church-thesis.tex @@ -85,4 +85,4 @@ eines nämlich, welches Entscheidungsprobleme lösen kann, die die TM nicht kann Wir nehmen also (wie in vielen Bereichen der Physik (die Relativitätstheorie ist ein gutes Beispiel) und Mathematik) und postulieren sie als Axiom. -\shade{Orange}{Fun fact} Die Church'sche These ist das einzige informatikspezifische Axiom. +\shade{Orange}{Fun fact} Die Church'sche These ist das Einzige informatikspezifische Axiom. diff --git a/semester3/ti/ti-summary.pdf b/semester3/ti/ti-summary.pdf index 4ca408e7b13471a893be2ec72b687850c10cc965..a60e8ecbb96aea8cf542ad276fd4fec05a678c42 100644 GIT binary patch delta 40548 zcmV)YK&-#^!aA?SI}bKyC!Zr@$Kzd(9+d;9*_MG%0ZQbibkY^c!Mg%5=F z>HmXE<&zbSrSF3eSyjOm3a%(zRg?@CNQfYrLX9>}Q9Xw5(srH~f0dU=*X>B6ekme? 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