--- a/hws/hw07.tex Mon Nov 11 00:34:14 2013 +0000
+++ b/hws/hw07.tex Mon Nov 11 13:48:34 2013 +0000
@@ -13,28 +13,12 @@
\section*{Homework 7}
\begin{enumerate}
-\item Suppose the following finite deterministic automaton over the alphabet $\{0, 1\}$.
+\item Suppose the following grammar for positive numbers
\begin{center}
-\begin{tikzpicture}[scale=2, line width=0.5mm]
- \node[state, initial, accepting] (q0) at ( 0,1) {$q_0$};
- \node[state, accepting] (q1) at ( 1,1) {$q_1$};
- \node[state] (q2) at ( 2,1) {$q_2$};
- \path[->] (q0) edge[bend left] node[above] {$0$} (q1)
- (q1) edge[bend left] node[above] {$1$} (q0)
- (q2) edge[bend left=50] node[below] {$1$} (q0)
- (q1) edge node[above] {$0$} (q2)
- (q2) edge [loop right] node {$0$} ()
- (q0) edge [loop below] node {$1$} ()
- ;
-\end{tikzpicture}
+
\end{center}
-Give a regular expression that can recognise the same language as
-this automaton. (Hint: If you use Brzozwski's method, you can assume
-Arden's lemma which states that an equation of the form $q = q\cdot r + s$
-has the unique solution $q = s \cdot r^*$.)
-
\item Consider the following grammar
\begin{center}