--- a/hws/hw03.tex	Fri Oct 10 12:26:29 2025 +0100
+++ b/hws/hw03.tex	Sat Oct 11 08:33:35 2025 +0100
@@ -88,8 +88,8 @@
 
 
       \solution{
-        A formula for DFAs is
-
+s        A formula for DFAs is
+eed
         \[L(A) \dn \{s \;|\; \hat{\delta}(start_q, s) \in F\}\]
 
         For NFAs you need to first define what $\hat{\rho}$ means. If
@@ -275,12 +275,12 @@
 \item On Mentimeter there was a question: \textit{``Why does the [regex] $(a^*)^*b$ takes much longer for 
 strings of length 28 compared to say 25?''}\smallskip\\
 
-For this consider a lake with $1000 m^3$ surface and an invasive plant
+For this consider a lake with $1000 m^2$ surface and an invasive plant
 that tries to cover the lake with leaves, think of the famous  water lily that
 produces leaves on which you can stand. This plant starts out with a
-seedling covering just $0.001 m^3$ of the lake, but doubles every day
-the surface that is covers. So on day two it would cover $0.002 m^3$,
-on day three $0.004 m^3$ and so on. How many days does the plant need to 
+seedling covering just $0.001 m^2$ of the lake, but doubles every day
+the surface that is covers. So on day two it would cover $0.002 m^2$,
+on day three $0.004 m^2$ and so on. How many days does the plant need to 
 cover the entire lake? How many days is the lake still 90\% \emph{un}covered? 
 
 \solution{That is a classic example of the law of exponentiation, meaning an