From 4bb517a0f08591ea91937a1dec4aefd7caade3d0 Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Sat, 4 Oct 2025 11:28:46 +0200 Subject: [PATCH] [TI] Catch up to current state --- .../02_finite-automata/01_simulations.tex | 19 ++++++++++++++++++ semester3/ti/ti-summary.pdf | Bin 836110 -> 851961 bytes semester3/ti/ti-summary.tex | 7 +++++-- 3 files changed, 24 insertions(+), 2 deletions(-) diff --git a/semester3/ti/parts/02_finite-automata/01_simulations.tex b/semester3/ti/parts/02_finite-automata/01_simulations.tex index 5e84608..fb471be 100644 --- a/semester3/ti/parts/02_finite-automata/01_simulations.tex +++ b/semester3/ti/parts/02_finite-automata/01_simulations.tex @@ -1,4 +1,23 @@ % Starting P63 = P78 \newpage \subsection{Simulationen} +Der Begriff der Simulation ist nicht ein formalisiert, da er je nach Fachgebiet, eine etwas andere Definition hat. +Die engste Definition fordert, dass jeder elementare Schritt der zu Berechnung, welche simuliert wird, durch eine Berechnung in der Simulation nachgemacht wird. +Eine etwas schwächere Forderung legt fest, dass in der Simulation auch mehrere Schritte verwendet werden dürfen. +Es gibt auch eine allgemeinere Definition, die besagt, dass nur das gleiche Eingabe-Ausgabe-Verhalten gilt und der Weg, oder die Berechnungen, welche die Simulation geht, respektive durchführt, wird ignoriert, respektive wird nicht durch die Definition beschränkt. + +\textit{Hier werden wir aber die enge Definition verwenden} + +\inlinelemma Wir haben zwei EA $M_1 = (Q_1, \Sigma, \delta_1, q_{01}, F_1)$ und $M_2 = (Q_2, \Sigma, \delta_2, q_{02}, F_2)$, die auf dem Alphabet $\Sigma$ operieren. +Für jede Mengenoperation $\odot \in \{ \cup, \cap, - \}$ existiert ein EA $M$, so dass $L(M) = L(M_1) \odot L(M_2)$ + +Was dieses Lemma nun aussagt ist folgendes: Man kann einen endlichen Automaten bauen, so dass das Verhalten von zwei anderen EA im Bezug auf die Mengenoperation simuliert wird. +Ein guter, ausführlicher Beweis dieses Lemmas findet sich im Buch auf Seite 64 (= Seite 79 im PDF) + +Dieses Lemma hat weitreichende Nutzen. Besonders ist es also möglich einen modularen EA zu bauen, in dem Teile davon in kleinere und einfachere EA auszulagern, die dann wiederverwendet werden können. + +\stepcounter{examples} +\inlineex Dieses Beispiel im Buch ist sehr gut erklärt und findet sich auf Seiten 65, 66 \& 67 (= Seite 80, 81 \& 82 im PDF) + +% TODO: Continue from page 83 (PDF) diff --git a/semester3/ti/ti-summary.pdf b/semester3/ti/ti-summary.pdf index c1a76a840ac238ea957cf953fcff3e012934340d..298244e3ce430242278ab51dfc1bd665ccb3e1cf 100644 GIT binary patch delta 118075 zcmZs>Q*hwT6E3{5osDhVwr$(m*vT(8H@0otcCzut&c-&r_kX^Nb91WZ>FS#4nTzSE zn(n7NE`;^w2S2S7lvW6ZP_IV+Jg1h`Wu$s1LIG1aQ zCxL2oCc($J`nck5`YP!0N!U7cII(`%7I_)S$`U~wVU;wKIgw@P#1YD5uUPoC+!By_xAITb*PLaC!3)}UL*@d4nF5`zo>czKl$k4Tt&yl}aSh8&h z_Dlp*go-&g>S_4Ux0BxrVD|pU0KqP5ybO!k`)8=1D36}%Q7{g(49dyF6gv*{9gcWO zdA%ut9RmiCmy&utvT{CL5E)>}_C-l5)UW647$cM*1r5s&&5|w*MvCJ^Jm9mx7RWM1 zf!D2wHZppcLhd3~tYpTw?NwlGLuM`)UCC9Oh!QD+nPL46&NnGy;S<4lVsysDU) 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zE=ko`VWCE<)(SVvQgv2;xc$6TV#Q=-U*3ur{*+3sc>Pl4`Q7;}fZ7%LeaAwOBTMORCkf z(O;z6EStX-|H`LA#D#%~XJ3hU?z@N=eu{YM*NB&Yi+Hs*;*G&oh{cN$moG)U{e8qc zS0dh>kGT4A#I-vS*E=IVEJu9AlRq7c_&k2e?8_JR-YVDu4ud0L1dM{CU<`}{jr%w_ q0ZxJmFbPgs_SFaR$v1|={~C|!pO?`83>^$JG&nan3MC~)Peux-q>w8B diff --git a/semester3/ti/ti-summary.tex b/semester3/ti/ti-summary.tex index b1fcb2f..fa25379 100644 --- a/semester3/ti/ti-summary.tex +++ b/semester3/ti/ti-summary.tex @@ -32,7 +32,7 @@ \begin{center} HS2025, ETHZ\\[0.2cm] \begin{Large} - Summary of the book \color{MidnightBlue}\fbox{\href{https://link.springer.com/book/10.1007/978-3-658-06433-4}{Theoretische Informatik}}\color{black} + Summary of the book \color{MidnightBlue}\fbox{\href{https://link.springer.com/book/10.1007/978-3-658-06433-4}{Theoretische Informatik}}\color{black} \end{Large}\\[0.2cm] by Prof. Dr. Juraj Hromkovic \end{center} @@ -42,7 +42,10 @@ \printtoc{Orange} \begin{scriptsize} - \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)} + \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 $P_{\text{PDF}} = P_{\text{Book}} + 15$} + \end{itemize} \end{scriptsize} \newpage