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\noindent \large{(10) \textbf{Zadatak 1.}\ \emph{Konstruirajte DKA koji prepoznaje jezik\\
L $= \{ w \in (a+b)^* |$ rije\v{c} po\v{c}inje i zavr\v{s}ava istim
slovom, te sadr\v{z}i rije\v{c} \textit{bab} \}. Koji regularni izraz opisuje jezik L? }\\

 DKA:\\
\includegraphics{automat1a.jpeg}
\\
 regularni izraz:\\
$bab + a(a+b)^\ast bab(a+b)^\ast a + b(a+b)^\ast bab (a+b)^\ast b$\\
\newpage


\noindent \large{(10) \textbf{Zadatak 2.}\ \emph{Za dani regularni izraz algoritamski konstruirajte NDKA koji prepoznaje pripadni jezik.}\\
$((ab^\ast + ba^\ast )^\ast + (c^\ast a + a^\ast c)^\ast)bac$\\
\includegraphics{automat2.jpeg}
\includegraphics{automat2b.jpeg}
\includegraphics{automat2d.jpeg}
\includegraphics{automat2e.jpeg}
\includegraphics{automat2f.jpeg}
\newpage


\noindent \large{(10) \textbf{Zadatak 3.}\ \emph{Dani NDKA prebacite u ekvivalentni DKA. Te za dobiveni DKA konstruirati skupovne jednad\v{z}be.}\\
N\ldots\\
\includegraphics{automat3ndka.jpeg}
\\
$N=(\{A,B,C\}, \{a,b\}, \delta, \{B\}, \{A\} )$\\
$M=(\{2^{A,B,C}\}, \{a,b\}, \delta', \{A,B\}, \{ \{A\},\{AB\},\{AC\},\{ABC\}\} )$\\
\\
\\
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
& A & B & C & AB & AC & BC & ABC \\
\hline
a & AB & C & AC & ABC & ABC & AC & ABC\\
b & BC & B & AC & BC & ABC & ABC & ABC\\
\hline
\end{tabular}\\

\includegraphics{automat3dka.jpeg}
\\

skupovne jednad\v{z}be:\\
\\
$B=bB+aC\\
C=(a+b)AC\\
AC=(a+b)ABC\\
ABC=(a+b)ABC+\epsilon$
\newpage

\noindent \large{\textbf{Zadatak 8.}\ \emph{Opi\v{s}ite rije\v{c}ima najmanje 3 jezika te za njih konstrurajte regularne izraze.}\\
\\

a) $L_1=\{w | w=w_1,\ldots,w_k  w_i \in \{1,2,3,4,5,6\},$ iza svakog
neparnog broja mora biti neki parni\}\\
\\
$A_N=\{1,3,5\}$\\
$A_P = \{2,4,6\}$\\

$A_P^{\ast}(A_N A_P)$\\
\\

b) $L_2=\{w | w$ je datum oblika dan.mjesec, dan $\in$
\{1,2,3,\ldots,31\}, mjesec $\in$ \{sje\v{c}anj, velja\v{c}a,
\ldots, prosinac\} \}\\
napomena: nije potrebno uzimati u obzir prijestupne godine.\\
\\
$d_1=$\{1,2,3,\ldots,28\}\\
$d_2=$\{30\}\\
$d_3=$\{31\}\\
t=\{.\}\\
$m_1=$\{sje\v{c}anj, velja\v{c}a,
\ldots, prosinac\}\\
$m_2=$\{sje\v{c}anj, o\v{z}ujak,
\ldots, prosinac\}\\
$m_3=$\{sje\v{c}anj, o\v{z}ujak, svibanj, srpanj, kolovoz,
listopad, prosinac\}\\

$d_1 t m_1 + d_2 t m_2 + d_3 t m_3$\\
\\

c) $L=\{w| w \in \{a,b,c,\ldots,z\}, |w| \neq 0$ ne smije poceti
samoglasnikom,
ne smije zavr\v{s}iti suglasnikom\}\\
\\
$A=\{a,b,c,\ldots,z\}$\\
$SA=\{a,e,i,o,u\}$\\
$SU=A\backslash SA$\\

$SU^+ A\ast SA^+$\\


\flushright Petra Dunkel

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