forked from klausuren/klausuren-allgemein
60 lines
2.2 KiB
TeX
60 lines
2.2 KiB
TeX
\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} |