--- a/hws/hw03.tex Sat Oct 03 00:51:47 2020 +0100
+++ b/hws/hw03.tex Sat Oct 03 15:21:06 2020 +0100
@@ -173,10 +173,21 @@
has the unique solution $q = s \cdot r^*$.)
\item If a non-deterministic finite automaton (NFA) has
-$n$ states. How many states does a deterministic
-automaton (DFA) that can recognise the same language
-as the NFA maximal need?
+ $n$ states. How many states does a deterministic
+ automaton (DFA) that can recognise the same language
+ as the NFA maximal need?
+\item Prove that for all regular expressions $r$ we have
+
+\begin{center}
+ $\textit{nullable}(r) \quad \text{if and only if}
+ \quad [] \in L(r)$
+\end{center}
+
+ Write down clearly in each case what you need to prove
+ and what are the assumptions.
+
+
\item \POSTSCRIPT
\end{enumerate}