--- a/handouts/ho01.tex	Mon Aug 30 15:50:27 2021 +0100
+++ b/handouts/ho01.tex	Tue Aug 31 11:49:09 2021 +0100
@@ -42,13 +42,13 @@
 
 
 \begin{document}
-\fnote{\copyright{} Christian Urban, King's College London, 2014, 2015, 2016, 2017, 2018, 2019, 2020}
+\fnote{\copyright{} Christian Urban, King's College London, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021}
 
 \section*{Handout 1}
 
 
 The purpose of a compiler is to transform a program a human can read and
-write into code the machine can run as fast as possible. Developing a
+write into code machines can run as fast as possible. Developing a
 compiler is an old craft going back to 1952 with the first compiler
 written by Grace Hopper.\footnote{Who many years ago was invited on a
 talk show hosted by David Letterman.
@@ -344,7 +344,7 @@
 
 \noindent
 Finally, on 2 July 2019 Cloudflare had a global outage because of a 
-regular expression (they had no outage for the last 6 years).  What
+regular expression (they had no outage for the 6 years before).  What
 happened is nicely explained in the blog:
 
 \begin{center}
@@ -531,7 +531,7 @@
 If you prefer to think in terms of the implementation
 of regular expressions in Scala, the constructors and
 classes relate as follows\footnote{More about Scala is 
-in the handout about \emph{A Crash-Course on Scala}.}
+in the handout about \emph{A Crash-Course on Scala} from PEP.}
 
 \begin{center}
 \begin{tabular}{rcl}
@@ -621,6 +621,8 @@
                      & = & L(r_1 + (r_2 + r_3))
 \end{eqnarray*}
 
+\noindent
+That means both languages are the same.
 The point of the definition of $L$ is that we can use it to
 precisely specify when a string $s$ is matched by a regular
 expression $r$, namely if and only if $s \in L(r)$. In fact we
@@ -715,7 +717,7 @@
 expressions and the notion of derivatives. Earlier versions of
 this theorem used always automata in the proof. Using this
 theorem we can show that regular languages are closed under
-complementation, something which Gasarch in his
+complementation, something which Bill Gasarch in his Computational Complexity
 blog\footnote{\url{http://goo.gl/2R11Fw}} assumed can only be
 shown via automata. So even somebody who has written a 700+-page
 book\footnote{\url{http://goo.gl/fD0eHx}} on regular