diff -r 4dbeaf43031d -r b9b54574ee41 hws/hw03.tex --- a/hws/hw03.tex Sat Oct 11 13:50:36 2014 +0100 +++ b/hws/hw03.tex Sat Oct 11 13:54:18 2014 +0100 @@ -67,28 +67,7 @@ \end{tikzpicture} \end{center} -\item Given the following deterministic finite automaton over the - alphabet $\{0, 1\}$, find the corresponding minimal automaton. In - case states can be merged, state clearly which states can be merged. - \begin{center} - \begin{tikzpicture}[scale=2, line width=0.7mm] - \node[state, initial] (q0) at ( 0,1) {$q_0$}; - \node[state] (q1) at ( 1,1) {$q_1$}; - \node[state, accepting] (q4) at ( 2,1) {$q_4$}; - \node[state] (q2) at (0.5,0) {$q_2$}; - \node[state] (q3) at (1.5,0) {$q_3$}; - \path[->] (q0) edge node[above] {$0$} (q1) - (q0) edge node[right] {$1$} (q2) - (q1) edge node[above] {$0$} (q4) - (q1) edge node[right] {$1$} (q2) - (q2) edge node[above] {$0$} (q3) - (q2) edge [loop below] node {$1$} () - (q3) edge node[left] {$0$} (q4) - (q3) edge [bend left=95, looseness = 2.2] node [left=2mm] {$1$} (q0) - (q4) edge [loop right] node {$0, 1$} (); - \end{tikzpicture} - \end{center} %\item Given the following deterministic finite automaton % @@ -124,6 +103,29 @@ \end{tikzpicture} \end{center} +\item Given the following deterministic finite automaton over the + alphabet $\{0, 1\}$, find the corresponding minimal automaton. In + case states can be merged, state clearly which states can be merged. + + \begin{center} + \begin{tikzpicture}[scale=2, line width=0.7mm] + \node[state, initial] (q0) at ( 0,1) {$q_0$}; + \node[state] (q1) at ( 1,1) {$q_1$}; + \node[state, accepting] (q4) at ( 2,1) {$q_4$}; + \node[state] (q2) at (0.5,0) {$q_2$}; + \node[state] (q3) at (1.5,0) {$q_3$}; + \path[->] (q0) edge node[above] {$0$} (q1) + (q0) edge node[right] {$1$} (q2) + (q1) edge node[above] {$0$} (q4) + (q1) edge node[right] {$1$} (q2) + (q2) edge node[above] {$0$} (q3) + (q2) edge [loop below] node {$1$} () + (q3) edge node[left] {$0$} (q4) + (q3) edge [bend left=95, looseness = 2.2] node [left=2mm] {$1$} (q0) + (q4) edge [loop right] node {$0, 1$} (); + \end{tikzpicture} + \end{center} + \item Given the following finite deterministic automaton over the alphabet $\{a, b\}$: \begin{center}