--- a/handouts/ho05.tex	Wed Nov 06 15:04:40 2019 +0000
+++ b/handouts/ho05.tex	Wed Nov 06 17:09:58 2019 +0000
@@ -459,7 +459,39 @@
 
 To answer the question about complexity, let me describe next the CYK
 algorithm (named after the authors Cocke–Younger–Kasami). This algorithm
-works with grammars that are in Chomsky normalform. 
+works with grammars that are in \emph{Chomsky normalform}. In Chomsky
+normalform all rules must be of the form $\meta{A} ::= a$, where $a$ is 
+a terminal, or $\meta{A} ::= \meta{B}\cdot \meta{C}$, where $\meta{B}$ and
+$\meta{B}$ need to be non-terminals. And no rule can contain $\epsilon$.
+The following grammar is in Chomsky normalform:
+
+\begin{plstx}[margin=1cm]
+  : \meta{S\/} ::= \meta{N}\cdot \meta{P}\\
+  : \meta{P\/} ::= \meta{V}\cdot \meta{N}\\
+  : \meta{N\/} ::= \meta{N}\cdot \meta{N}\\
+  : \meta{N\/} ::= \meta{A}\cdot \meta{N}\\
+  : \meta{N\/} ::= \texttt{student} | \texttt{trainer} | \texttt{team} 
+                   | \texttt{trains}\\
+  : \meta{V\/} ::= \texttt{trains} | \texttt{team}\\
+  : \meta{A\/} ::= \texttt{The} | \texttt{the}\\
+\end{plstx}
+
+\noindent
+where $\meta{S}$ is the start symbol and $\meta{S}$, $\meta{P}$,
+$\meta{N}$, $\meta{V}$ and $\meta{A}$ are non-terminals. The ``words''
+are terminals. The rough idea behind this grammar is that $\meta{S}$
+stands for a sentence, $\meta{P}$ is a predicate, $\meta{N}$ is a noun
+and so on. For example the rule \mbox{$\meta{P} ::= \meta{V}\cdot
+\meta{N}$} states that a predicate can be a verb followed by a noun.
+Now the question is whether the string 
+
+\begin{center}
+  \texttt{The trainer trains the student team}
+\end{center}
+
+\noindent
+is recognised by the grammar. The CYK algorithm starts with the
+following triangular data structure.
 
 TBD