--- a/hws/hw04.tex	Fri Oct 16 14:27:20 2015 +0100
+++ b/hws/hw04.tex	Sat Oct 17 11:24:41 2015 +0100
@@ -68,13 +68,34 @@
   (Hint: You can assume you are already given a regular expression written \texttt{ALL},
   that can recognise any character, and a regular expression \texttt{NOT} that recognises
   the complement of a regular expression.)
+  
+\item Simplify the regular expression
 
-\item How many basic regular expressions are there to match the string
-  $abcd$? (ii) How many if they cannot include $\epsilon$ and
-  $\varnothing$? (iii) How many if they are also not allowed to
-  contain stars? (iv) How many if they are also not allowed to contain
-  $\_ + \_$?
+\[
+(\varnothing \cdot (b \cdot c)) + 
+((\varnothing \cdot c) + \epsilon)
+\]
+
+Does simplification always preserve the meaning of a regular
+expression? 
+     
+\item The Sulzmann algorithm contains the function $mkeps$
+      which answers how a regular expression can match the
+      empty string. What is the answer of $mkeps$ for the
+      regular expressions:    
 
+  \[
+  \begin{array}{l}
+  (\varnothing \cdot (b \cdot c)) + 
+  ((\varnothing \cdot c) + \epsilon)\\
+  (a + \varepsilon) \cdot (\varepsilon + \varepsilon)
+  \end{array}
+  \]
+
+\item What is the purpose of the record regular expression
+  in the Sulzmann algorithm?
+  
+  
 %\item (Optional) The tokenizer in \texttt{regexp3.scala} takes as
 %argument a string and a list of rules. The result is a list of tokens. Improve this tokenizer so 
 %that it filters out all comments and whitespace from the result.