hws/hw03.tex
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   171   this automaton. (Hint: If you use Brzozwski's method, you can assume
   171   this automaton. (Hint: If you use Brzozwski's method, you can assume
   172   Arden's lemma which states that an equation of the form $q = q\cdot r + s$
   172   Arden's lemma which states that an equation of the form $q = q\cdot r + s$
   173   has the unique solution $q = s \cdot r^*$.)
   173   has the unique solution $q = s \cdot r^*$.)
   174 
   174 
   175 \item If a non-deterministic finite automaton (NFA) has
   175 \item If a non-deterministic finite automaton (NFA) has
   176 $n$ states. How many states does a deterministic 
   176   $n$ states. How many states does a deterministic 
   177 automaton (DFA) that can recognise the same language
   177   automaton (DFA) that can recognise the same language
   178 as the NFA maximal need?
   178   as the NFA maximal need?
   179 
   179 
       
   180 \item Prove that for all regular expressions $r$ we have
       
   181       
       
   182 \begin{center} 
       
   183   $\textit{nullable}(r) \quad \text{if and only if} 
       
   184   \quad [] \in L(r)$ 
       
   185 \end{center}
       
   186 
       
   187       Write down clearly in each case what you need to prove
       
   188       and what are the assumptions. 
       
   189 
       
   190   
   180 \item \POSTSCRIPT  
   191 \item \POSTSCRIPT  
   181 \end{enumerate}
   192 \end{enumerate}
   182 
   193 
   183 \end{document}
   194 \end{document}
   184 
   195