hws/hw05.tex
changeset 527 2a62f0845f98
parent 444 3056a4c071b0
child 602 9aa901039e33
equal deleted inserted replaced
526:a6093b0ad246 527:2a62f0845f98
     1 \documentclass{article}
     1 \documentclass{article}
     2 \usepackage{../style}
     2 \usepackage{../style}
     3 \usepackage{../graphics}
     3 \usepackage{../graphics}
     4 
     4 \usepackage{../grammar}
     5 
     5 
     6 \begin{document}
     6 \begin{document}
     7 
     7 
     8 % explain what is a context-free grammar and the language it generates 
     8 % explain what is a context-free grammar and the language it generates 
     9 %
     9 %
    86 
    86 
    87 In case they can, give the corresponding token sequences. (Hint: 
    87 In case they can, give the corresponding token sequences. (Hint: 
    88 Observe the maximal munch rule and the priorities of your regular
    88 Observe the maximal munch rule and the priorities of your regular
    89 expressions that make the process of lexing unambiguous.)
    89 expressions that make the process of lexing unambiguous.)
    90 
    90 
       
    91 \item Given the following context-free grammar $G$
       
    92   
       
    93 \begin{plstx}[margin=1cm]
       
    94   : \meta{S\/} ::= \meta{A\/}\cdot\meta{S\/}\cdot\meta{B\/} \;\mid\;
       
    95                    \meta{B\/}\cdot\meta{S\/}\cdot\meta{A\/} \;\mid\; \epsilon\\
       
    96   : \meta{A\/} ::= a \mid \epsilon\\
       
    97   : \meta{B\/} ::= b\\
       
    98 \end{plstx}
       
    99 
       
   100 which of the following strings are in the language of $G$?
       
   101 
       
   102 \begin{itemize}
       
   103 \item[$\bullet$] $a$
       
   104 \item[$\bullet$] $b$
       
   105 \item[$\bullet$] $ab$
       
   106 \item[$\bullet$] $ba$
       
   107 \item[$\bullet$] $bb$
       
   108 \item[$\bullet$] $baa$
       
   109 \end{itemize}  
       
   110 
       
   111 
    91 \item {\bf(Optional)} Recall the definitions for $Der$ and $der$
   112 \item {\bf(Optional)} Recall the definitions for $Der$ and $der$
    92       from the lectures. Prove by induction on $r$ the
   113       from the lectures. Prove by induction on $r$ the
    93       property that 
   114       property that 
    94 
   115 
    95 \[
   116 \[