From dad93acda80397abc34b5170954dba3de617ccde Mon Sep 17 00:00:00 2001 From: Hendrik Cech Date: Tue, 27 Jun 2017 20:27:17 +0200 Subject: [PATCH] Add GdI-GTI-B WS16/17 --- GdI-GTI-B/WS1617 GTI.tex | 60 +++++++++++++++++++++++++++++ GdI-GTI-B/WS1617-GTI_Diagram_1.png | Bin 0 -> 353929 bytes GdI-GTI-B/WS1617-GTI_Diagram_2.png | Bin 0 -> 231081 bytes 3 files changed, 60 insertions(+) create mode 100644 GdI-GTI-B/WS1617 GTI.tex create mode 100644 GdI-GTI-B/WS1617-GTI_Diagram_1.png create mode 100644 GdI-GTI-B/WS1617-GTI_Diagram_2.png diff --git a/GdI-GTI-B/WS1617 GTI.tex b/GdI-GTI-B/WS1617 GTI.tex new file mode 100644 index 0000000..d69a2af --- /dev/null +++ b/GdI-GTI-B/WS1617 GTI.tex @@ -0,0 +1,60 @@ +\input{../settings/settings} + +\usepackage{amsmath} + +\begin{document} + \klausur{GdI-GTI-B Machines and Languages} + {Prof. M. Mendler, Ph.D.} + {Wintersemester 16/17} + {90} + {Wörterbuch (Englisch-Deutsch/Deutsch-Englisch)} + + \begin{enumerate} + \item{ + Consider the following non-deterministic automaton $M$ over input alphabet + $\Sigma = \{a,b\}$: + \image{0.6}{WS1617-GTI_Diagram_1.png}{NDA $M$}{NDA $M$} + \begin{enumerate} + \item Construct a \textbf{deterministic} automaton $M'$ that accepts the + same language, i.e., such that $L(M') = L(M)$. + \item Find a regular expression $r$ that represents the language of the + automaton $M$ (and $M'$), i.e., so that $L(r) = L(M) = L(M')$. + \end{enumerate} + + Make sure you \textbf{explain} how you obtained your answer in each of + the sub-questions! + } + + \item{ + Consider the following pushdown automaton (PDA) $M$ over input alphabet + $\Sigma = \{0,1\}$ and stack alphabet $\Gamma = \{0, \#\}$: + \image{0.8}{WS1617-GTI_Diagram_2.png}{PDA $M$}{PDA $M$} + + Give a formal (or an informal but precise) description of the language + $L(M) \subseteq \{0,1\}^*$ that is accepted by $M$ and \textbf{justify + your answer} by referring to the operational behavior of $M$ as + specified by the transition diagram given for $M$ above. + } + + \item{ + Consider the context-free grammar $G = (\{S, B\}, \{a,b\}, S, P)$ with + production rules $P$ given as: + \begin{align*} + S \quad &\rightarrow \quad aSaB \; | \; aaB \\ + B \quad &\rightarrow \quad bB \; | \; \Delta + \end{align*} + + \begin{enumerate} + \item The word $w = aaaabaabb$ is a word of the language $L_G = L(G)$ + generated b grammar $G$. Draw a derivation tree (parse tree) for $w$ + with respect to $G$. + \item Construct a pushdown automaton $M_G$ that accepts the same language, + ,i.e., for which $L(M_G) = L(G)$. + \end{enumerate} + } + \item What is \textit{Cook's Theorem} and what is its significance in + complexity theory? + \end{enumerate} +\end{document} + + %\image{1}{Capture3.PNG}{DNS-Anfrage}{DNS-Anfrage} \ No newline at end of file diff --git a/GdI-GTI-B/WS1617-GTI_Diagram_1.png b/GdI-GTI-B/WS1617-GTI_Diagram_1.png new file mode 100644 index 0000000000000000000000000000000000000000..b6cc58370f13699ff1b696a2eb4abd246b7754d3 GIT binary patch literal 353929 zcmZ^}cUV(V(=Un@QHlrxQdN*5(nNZR3JORQK|nf0L8TKQKp;^8k*w| zHBuur^Z_3W8@cW-EEP|}B^zFHg49N_Ez%IgISi*58~XpGHe^9=7G zoMGc~E+{1zG;~!%T!WYk;yn2-?opb=`EwsG-C#R^{lka2I743U2i|jxwhUEhmNgEQ=t97!em%nT2@0OGWVy&Ie8uN$aj&Zf>DOEPGq!in7`{>b z;!pW-Zd_4W`K%!wa18SW5KinC!>;e3vCLy8v(6$c>_G?%OV%~pdGR~im)aZ7)yBoL zA4l?YoA4yvI^V7ZtHe077cgB8V2YhMC2KyrbGj#3^2Y|{W?5O>Lc4~zHy0zR*J@9( 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