--- a/handouts/ho03.tex	Sat Oct 22 13:11:33 2016 +0100
+++ b/handouts/ho03.tex	Sat Oct 22 15:18:11 2016 +0100
@@ -17,7 +17,7 @@
 widely known rather recently. Still let us in this lecture
 have a closer look at automata and their relation to regular
 expressions. This will help us with understanding why the
-regular expression matchers in Python and Ruby are so slow
+regular expression matchers in Python, Ruby and Java are so slow
 with certain regular expressions. The central definition
 is:\medskip 
 
@@ -177,7 +177,8 @@
 have to ``consume'' any part of the input string, but
 ``silently'' change to a different state. In the left picture,
 for example, if you are in the starting state, you can 
-silently move either to $q_1$ or $q_2$.
+silently move either to $q_1$ or $q_2$. This silent
+transition is also often called \emph{$\epsilon$-transition}.
 
 
 \subsubsection*{Thompson Construction}
@@ -558,7 +559,7 @@
 constructed. First have a look at the second equation: the
 left-hand side is $q_1$ and the right-hand side $q_0\,a$. The
 right-hand side is essentially all possible ways how to end up
-in $q_1$. There is only one incoming edge from $q_0$ consuming
+in node $q_1$. There is only one incoming edge from $q_0$ consuming
 an $a$.  Therefore the right hand side is this
 state followed by character---in this case $q_0\,a$. Now lets
 have a look at the third equation: there are two incoming