Add GdI-GTI-B WS16/17

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}