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103 |
103 |
104 Give a regular expression that can recognise the same language as |
104 Give a regular expression that can recognise the same language as |
105 this automaton. (Hint: If you use Brzozwski's method, you can assume |
105 this automaton. (Hint: If you use Brzozwski's method, you can assume |
106 Arden's lemma which states that an equation of the form $q = q\cdot r + s$ |
106 Arden's lemma which states that an equation of the form $q = q\cdot r + s$ |
107 has the unique solution $q = s \cdot r^*$.)\ |
107 has the unique solution $q = s \cdot r^*$.)\ |
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108 |
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109 \item Recall the definitions for $Der$ and $der$ from the lectures. |
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110 Prove by induction on $r$ the property that |
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111 |
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112 \[ |
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113 L(der\,c\,r) = Der\,c\,(L(r)) |
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114 \] |
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115 |
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116 holds. |
108 \end{enumerate} |
117 \end{enumerate} |
109 |
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110 |
118 |
111 \end{document} |
119 \end{document} |
112 |
120 |
113 %%% Local Variables: |
121 %%% Local Variables: |
114 %%% mode: latex |
122 %%% mode: latex |