From 51653841e7dc8ad75df8aca715e5c0f13f7c99be Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Mon, 10 Nov 2025 07:41:16 +0100 Subject: [PATCH] [TI] Compact: Clarifications & spelling fixes --- .../ti-compact/parts/01_words-alphabets.tex | 2 +- .../ti-compact/parts/02_finite-automata.tex | 4 ++-- semester3/ti-compact/ti-compact.pdf | Bin 332110 -> 332115 bytes 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/semester3/ti-compact/parts/01_words-alphabets.tex b/semester3/ti-compact/parts/01_words-alphabets.tex index e8e4ad0..5699d1f 100644 --- a/semester3/ti-compact/parts/01_words-alphabets.tex +++ b/semester3/ti-compact/parts/01_words-alphabets.tex @@ -60,7 +60,7 @@ where the Program doesn't have to compile, i.e. we can describe processes inform \fancydef{Randomness} $x \in \wordbool$ random if $K(x) \geq |x|$, thus for $n \in \N$, $K(n) \geq \ceil{\log_2(n + 1)} - 1$ \stepLabelNumber{theorem} -\fancytheorem{Prime number} $\displaystyle \limni \frac{\text{Prime}(n)}{\frac{n}{\ln(n)}}$ +\fancytheorem{Prime number} $\displaystyle \limni \frac{\text{Prime}(n)}{\frac{n}{\ln(n)}} = 1$ with $\text{Prime}(n)$ the number of prime numbers on $[0, n] \subseteq \N$ \fhlc{Cyan}{Proofs} Proofs in which we need to show a lower bound for Kolmogorov-Complexity (almost) always work as follows: Assume for contradiction that there are no words with $K(w) > f$ for all $w \in W$. diff --git a/semester3/ti-compact/parts/02_finite-automata.tex b/semester3/ti-compact/parts/02_finite-automata.tex index b04e909..dffdfc6 100644 --- a/semester3/ti-compact/parts/02_finite-automata.tex +++ b/semester3/ti-compact/parts/02_finite-automata.tex @@ -146,8 +146,8 @@ Thus, all four words have to lay in pairwise distinct states and we thus need at \subsection{Non-determinism} -The most notable differences between deterministic and non-deterministic FA is that the transition function maps is different: $\delta: Q \times \Sigma \rightarrow \cP(Q)$. -I.e., there can be any number of transitions for one symbol from $\Sigma$ from each state. +The most notable differences between deterministic and non-deterministic FA is that the transition function is different: $\delta: Q \times \Sigma \rightarrow \cP(Q)$. +I.e., there can be any number of transitions for one symbol of $\Sigma$ for each state. This is (in graphical notation) represented by arrows that have the same label going to different nodes. 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