Binary file hws/hw01.pdf has changed

--- a/hws/hw01.tex	Thu Sep 19 15:47:33 2024 +0100
+++ b/hws/hw01.tex	Thu Sep 19 16:32:26 2024 +0100
@@ -18,15 +18,20 @@
         \url{http://www.scala-lang.org}
       \end{center}
 
-       and the Ammonite REPL from
-
-       \begin{center}
-       \url{https://ammonite.io}
-       \end{center}      
+      % and the Ammonite REPL from
+      % 
+      % \begin{center}
+      % \url{https://ammonite.io}
+      % \end{center}      
 
       If you want to follow the code I present during the
-      lectures, read the handout about Scala. Make sure Ammonite
-      uses the Scala 3 compiler.
+      lectures, it might be useful to install VS Code or Codium.
+      I will be using Scala Version 3.5, which has the \texttt{scala-cli}
+      REPL used in PEP already built in.
+      
+      %handout about Scala.
+      %Make sure Ammonite
+      %uses the Scala 3 compiler.
 
 %\item {\bf (Optional)} Have a look at the crawler programs.
 %      Can you find a usage for them in your daily programming
@@ -71,13 +76,15 @@
       Is in general $A\,@\,B$ equal to $B\,@\,A$?
 
       \solution{ What is $A @ {[]}$? Are there special cases
-      where $A @ B = B @ A$? }
+        where $A @ B = B @ A$? Obviously when $A = B$ the stament is true.
+        But there are also cases when $A \not= B$, for example $A = \{a\}$
+      and $B = \{aaa\}$.}
 
 \item Assume a set $A$ contains 4 strings and a set $B$
       contains 7 strings. None of the strings is the empty
       string. How many strings are in $A \,@\, B$?
 
-      \solution{28, but there are corner cases where there are fewer
+      \solution{Everyone will probably answer with 28, but there are corner cases where there are fewer
         than 28 elements. Can students think of such corner cases?
       For example $A = \{a, ab, \ldots\}$, $B = \{bc, c,\ldots\}$ }
 
@@ -100,7 +107,8 @@
       allowed to contain stars? (4) How many if they are also
       not allowed to contain $\_ + \_$?
 
-      \solution{1-3 are infinite (tell the idea why - examples); 4 is five - remember regexes are trees.}
+      \solution{1-3 are infinite (tell the idea why and give examples);
+        4 is five - remember regexes are trees (that is the main point of the question.}
       
 \item When are two regular expressions equivalent? Can you
       think of instances where two regular expressions match
@@ -110,12 +118,17 @@
       $[b]$.
 
       \solution{for example $r^* = 1 + r \cdot r^*$ for any regular expression $r$.
-        Can students think about why this is the case?}
+        Can students think about why this is the case? - this would need a proof.}
 
 \item What is meant by the notions \emph{evil regular expressions}
   and by \emph{catastrophic backtracking}?
 
-  \solution{catastrophic backtracking also applies to other regexes, not just $(a^*)^*b$}
+  \solution{catastrophic backtracking also applies to other regexes,
+    not just $(a^*)^*b$.  Maybe
+    \url{https://www.trevorlasn.com/blog/when-regex-goes-wrong/} is
+    of help - even the CrowdStrike issue had an underlying problem
+    with a regex, though this one was not due to catastrophic
+    backtracking.}
 
 \item Given the regular expression $(a + b)^* \cdot b \cdot (a + b)^*$,
   which of the following regular expressions are equivalent