--- a/hws/hw03.tex	Wed Apr 06 12:18:54 2016 +0100
+++ b/hws/hw03.tex	Wed Apr 06 15:55:01 2016 +0100
@@ -9,28 +9,31 @@
 \HEADER
 
 \begin{enumerate}
-\item What is a regular language? Are there alternative ways to define this
-  notion? If yes, give an explanation why they define the same notion.
+\item What is a regular language? Are there alternative ways
+      to define this notion? If yes, give an explanation why
+      they define the same notion.
 
 \item Why is every finite set of strings a regular language?
 
-\item Assume you have an alphabet consisting of the letters $a$, $b$
-  and $c$ only. (1) Find a regular expression that recognises the two
-  strings $ab$ and $ac$. (2) Find a regular expression that matches
-  all strings \emph{except} these two strings. Note, you can only use
-  regular expressions of the form
+\item Assume you have an alphabet consisting of the letters
+      $a$, $b$ and $c$ only. (1) Find a regular expression
+      that recognises the two strings $ab$ and $ac$. (2) Find
+      a regular expression that matches all strings
+      \emph{except} these two strings. Note, you can only use
+      regular expressions of the form
       
   \begin{center} $r ::=
-    \varnothing \;|\; \epsilon \;|\; c \;|\; r_1 + r_2 \;|\;
+    \ZERO \;|\; \ONE \;|\; c \;|\; r_1 + r_2 \;|\;
     r_1 \cdot r_2 \;|\; r^*$ 
   \end{center}
 
-\item Define the function \textit{zeroable} which takes a regular
-  expression as argument and returns a boolean.  The function should
-  satisfy the following property:
+\item Define the function \textit{zeroable} which takes a
+      regular expression as argument and returns a boolean.
+      The function should satisfy the following property:
 
   \begin{center}
-    $\textit{zeroable(r)} \;\text{if and only if}\; L(r) = \varnothing$
+    $\textit{zeroable(r)} \;\text{if and only if}\; 
+    L(r) = \{\}$
   \end{center}
 
 \item Given the alphabet $\{a,b\}$. Draw the automaton that has two