
diff -r 4758a6155878 -r 1ab41c59e3d3 hw/hw06.tex
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+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
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-\documentclass{article}
-\usepackage{charter}
-\usepackage{hyperref}
-\usepackage{amssymb}
-\usepackage{amsmath}
-\usepackage{tikz}
-\usetikzlibrary{automata}
-
-\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
-
-\begin{document}
-
-\section*{Homework 6}
-
-\begin{enumerate}
-\item (i) Give the regular expressions for lexing a language
-consisting of whitespaces, identifiers (some letters followed by digits), numbers,
-operations \texttt{=}, \texttt{<} and \texttt{>}, and the keywords
-\texttt{if}, \texttt{then} and \texttt{else}.
-(ii) Decide whether the following strings 
-can be lexed in this language?
-
-\begin{enumerate}
-\item \texttt{"if y4 = 3 then 1 else 3"}
-\item \texttt{"if33 ifif then then23 else else 32"}
-\item \texttt{"if x4x < 33 then 1 else 3"}
-\end{enumerate}
-
-In case they can, give the corresponding token sequences. (Hint: 
-Observe the maximal munch rule and priorities of your regular
-expressions that make the process of lexing unambiguous.)
-
-\item Suppose the grammar
-
-\begin{center}
-\begin{tabular}{lcl}
-$E$ & $\rightarrow$ &  $F \;|\; F \cdot * \cdot F \;|\; F \cdot \backslash \cdot F$\\
-$F$ & $\rightarrow$ & $T \;|\; T \cdot \texttt{+} \cdot T \;|\; T \cdot \texttt{-} \cdot T$\\
-$T$ & $\rightarrow$ & $num \;|\; \texttt{(} \cdot E \cdot \texttt{)}$\\
-\end{tabular}
-\end{center}
-
-where $E$, $F$ and $T$ are non-terminals, $E$ is the starting symbol of the grammar, and $num$ stands for
-a number token. Give a parse tree for the string \texttt{(3+3)+(2*3)}.
-
-\item Define what it means for a grammar to be ambiguous. Give an example of
-an ambiguous grammar.
-
-\item Suppose boolean expressions are built up from
-
-\begin{center}
-\begin{tabular}{ll}
-1.) & tokens for \texttt{true} and \texttt{false},\\
-2.) & the infix operations \texttt{$\wedge$} and \texttt{$\vee$},\\
-3.) & the prefix operation $\neg$, and\\
-4.) & can be enclosed in parentheses.
-\end{tabular}
-\end{center}
-
-(i) Give a grammar that can recognise such boolean expressions
-and (ii) give a sample string involving all rules given in 1.-4.~that 
-can be parsed by this grammar.
-
-
-\end{enumerate}
-
-\end{document}
-
-%%% Local Variables: 
-%%% mode: latex
-%%% TeX-master: t
-%%% End: 




