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121 calculating the derivative, simplify all regular expressions as much |
121 calculating the derivative, simplify all regular expressions as much |
122 as possible, but at least apply the following six simplification |
122 as possible, but at least apply the following six simplification |
123 rules: |
123 rules: |
124 |
124 |
125 \begin{center} |
125 \begin{center} |
126 \begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}l} |
126 \begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}ll} |
127 $r \cdot \varnothing$ & $\mapsto$ & $\varnothing$\\ |
127 $r \cdot \varnothing$ & $\mapsto$ & $\varnothing$\\ |
128 $\varnothing \cdot r$ & $\mapsto$ & $\varnothing$\\ |
128 $\varnothing \cdot r$ & $\mapsto$ & $\varnothing$\\ |
129 $r \cdot \epsilon$ & $\mapsto$ & $r$\\ |
129 $r \cdot \epsilon$ & $\mapsto$ & $r$\\ |
130 $\epsilon \cdot r$ & $\mapsto$ & $r$\\ |
130 $\epsilon \cdot r$ & $\mapsto$ & $r$\\ |
131 $r + \varnothing$ & $\mapsto$ & $r$\\ |
131 $r + \varnothing$ & $\mapsto$ & $r$\\ |
132 $\varnothing + r$ & $\mapsto$ & $r$\\ |
132 $\varnothing + r$ & $\mapsto$ & $r$\\ |
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133 $r + r$ & $\mapsto$ & $r$ & (added on 12 October)\\ |
133 \end{tabular} |
134 \end{tabular} |
134 \end{center} |
135 \end{center} |
135 |
136 |
136 \noindent |
137 \noindent |
137 Write down your simplified derivative in the ``mathematicical'' |
138 Write down your simplified derivative in the ``mathematicical'' |