
diff -r ae039d6ae3f2 -r a1544b804d1e hws/hw05.tex
--- a/hws/hw05.tex	Mon Oct 06 20:55:16 2014 +0100
+++ b/hws/hw05.tex	Fri Oct 10 16:59:22 2014 +0100
@@ -10,6 +10,10 @@
 
 \begin{document}
 
+% explain what is a context-free grammar and the language it generates 
+%
+
+
 \section*{Homework 5}
 
 \begin{enumerate}
@@ -31,80 +35,7 @@
 $r ::= \varnothing \;|\; \epsilon \;|\; c  \;|\; r_1 + r_2  \;|\; r_1 \cdot r_2 \;|\; r^*$
 \end{center}
 
-\item Given a deterministic finite automata $A(Q, q_0, F, \delta)$, 
-define which language is recognised by this automaton.
 
-\item Given the following deterministic finite automata over the alphabet
-$\{a, b\}$, find an automaton that recognises the complement language.
-(Hint: Recall that for the algorithm from the lectures, the automaton needs to be
-in completed form, that is have a transition for every letter from the alphabet.) 
-
-\begin{center}
-\begin{tikzpicture}[scale=3, line width=0.7mm]
-  \node[state, initial]        (q0) at ( 0,1) {$q_0$};
-  \node[state, accepting]  (q1) at ( 1,1) {$q_1$};
-  \path[->] (q0) edge node[above] {$a$} (q1)
-                   (q1) edge [loop right] node {$b$} ()
-                  ;
-\end{tikzpicture}
-\end{center}
-
-\item Given the following deterministic finite automaton
-
-\begin{center}
-\begin{tikzpicture}[scale=3, line width=0.7mm]
-  \node[state, initial]        (q0) at ( 0,1) {$q_0$};
-  \node[state,accepting]  (q1) at ( 1,1) {$q_1$};
-  \node[state, accepting] (q2) at ( 2,1) {$q_2$};
-  \path[->] (q0) edge node[above] {$b$} (q1)
-                  (q1) edge [loop above] node[above] {$a$} ()
-                  (q2) edge [loop above] node[above] {$a, b$} ()
-                  (q1) edge node[above] {$b$} (q2)
-                  (q0) edge[bend right] node[below] {$a$} (q2)
-                  ;
-\end{tikzpicture}
-\end{center}
-find the corresponding minimal automaton. State clearly which nodes
-can be merged.
-
-\item Given the following non-deterministic finite automaton over the alphabet $\{a, b\}$,
-find a deterministic finite automaton that recognises the same language:
-
-\begin{center}
-\begin{tikzpicture}[scale=3, line width=0.7mm]
-  \node[state, initial]        (q0) at ( 0,1) {$q_0$};
-  \node[state]                    (q1) at ( 1,1) {$q_1$};
-  \node[state, accepting] (q2) at ( 2,1) {$q_2$};
-  \path[->] (q0) edge node[above] {$a$} (q1)
-                  (q0) edge [loop above] node[above] {$b$} ()
-                  (q0) edge [loop below] node[below] {$a$} ()
-                  (q1) edge node[above] {$a$} (q2)
-                  ;
-\end{tikzpicture}
-\end{center}
-
-\item
-Given the following finite deterministic automaton over the alphabet $\{a, b\}$:
-
-\begin{center}
-\begin{tikzpicture}[scale=2, line width=0.5mm]
-  \node[state, initial, accepting]        (q0) at ( 0,1) {$q_0$};
-  \node[state, accepting]                    (q1) at ( 1,1) {$q_1$};
- \node[state] (q2) at ( 2,1) {$q_2$};
-  \path[->] (q0) edge[bend left] node[above] {$a$} (q1)
-                  (q1) edge[bend left] node[above] {$b$} (q0)
-                  (q2) edge[bend left=50] node[below] {$b$} (q0)
-                  (q1) edge node[above] {$a$} (q2)
-                  (q2) edge [loop right] node {$a$} ()
-                  (q0) edge [loop below] node {$b$} ()
-            ;
-\end{tikzpicture}
-\end{center}
-
-Give a regular expression that can recognise the same language as
-this automaton. (Hint: If you use Brzozwski's method, you can assume
-Arden's lemma which states that an equation of the form $q = q\cdot r + s$
-has the unique solution $q = s \cdot r^*$.)\
 
 \item Recall the definitions for $Der$ and $der$ from the lectures. 
 Prove by induction on $r$ the property that 




