--- a/handouts/ho05.tex	Tue Oct 16 14:40:30 2018 +0100
+++ b/handouts/ho05.tex	Mon Oct 22 23:37:11 2018 +0100
@@ -17,8 +17,8 @@
 example for which there exists no regular expression is the
 language of well-parenthesised expressions. In languages like
 Lisp, which use parentheses rather extensively, it might be of
-interest whether the following two expressions are
-well-parenthesised (the left one is, the right one is not):
+interest to know whether the following two expressions are
+well-parenthesised or not (the left one is, the right one is not):
 
 \begin{center}
 $(((()()))())$  \hspace{10mm} $(((()()))()))$
@@ -29,7 +29,7 @@
 problems, we need more powerful techniques than regular
 expressions. We will in particular look at \emph{context-free
 languages}. They include the regular languages as the picture
-below shows:
+below about language classes shows:
 
 
 \begin{center}
@@ -46,10 +46,30 @@
 \end{tikzpicture}
 \end{center}
 
-\noindent Context-free languages play an important role in
-`day-to-day' text processing and in programming languages.
-Context-free languages are usually specified by grammars. For
-example a grammar for well-parenthesised expressions is
+\noindent Each ``bubble'' stands for sets of languages (remember
+languages are sets of strings). As indicated the set of regular
+languages are fully included inside the context-free languages,
+meaning every regular language is also context-free, but not vice
+versa. Below I will let you think for example what the context-free
+grammar is for the language corresponding to the regular expression
+$(aaa)^*a$.
+
+Because of their convenience, context-free languages play an important
+role in `day-to-day' text processing and in programming
+languages. Context-free in this setting means that ``words'' have one
+meaning only ansd this meaning is independend from in which context
+the ``words'' appear. For example ambiguity issues like
+
+\begin{center}
+\tt Time flies like an arrow; fruit flies like a banana.
+\end{center}  
+
+\noindent
+from natural languages were the meaning of \emph{flies} depend on the
+surounding \emph{context} are avoided as much as possible.
+
+Context-free languages are usually specified by grammars. For example
+a grammar for well-parenthesised expressions can be given as follows:
 
 \begin{plstx}[margin=3cm]
 : \meta{P} ::=  ( \cdot  \meta{P} \cdot ) \cdot \meta{P}
@@ -66,7 +86,8 @@
 
 In general grammars consist of finitely many rules built up
 from \emph{terminal symbols} (usually lower-case letters) and
-\emph{non-terminal symbols} (upper-case letters inside \meta{\mbox{}}). Rules have
+\emph{non-terminal symbols} (upper-case letters written in
+bold like \meta{A}, \meta{N} and so on). Rules have
 the shape
 
 \begin{plstx}[margin=3cm]