213 expressions and their ranking are shown above. 

   213 expressions and their ranking are shown above. For our algorithm it will  

   214 be helpful to have a look at the function \emph{zeroable}

   215 defined as follows:

   216 

   217 \begin{center}

   218 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}

   219 $zeroable(\varnothing)$      & $\dn$ & $true$\\

   220 $zeroable(\epsilon)$           & $\dn$ &  $f\!alse$\\

   221 $zeroable (c)$                    & $\dn$ &  $f\!alse$\\

   222 $zeroable (r_1 + r_2)$        & $\dn$ &  $zeroable(r_1) \wedge zeroable(r_2)$ \\ 

   223 $zeroable (r_1 \cdot r_2)$  & $\dn$ &  $zeroable(r_1) \vee zeroable(r_2)$ \\

   224 $zeroable (r^*)$                  & $\dn$ & $f\!alse$\\

   225 \end{tabular}

   226 \end{center}

   227 

   228 \noindent

   229 In contrast to the function $nullable(r)$, which test whether a regular expression

   230 can match the empty string, the $zeroable$ function identifies whether a regular

   231 expression cannot match anything at all. 

   232 

   233 \begin{center}

   234 \texttt{\Grid{$c_1$\VS{} true\VS{} then\VS{} x\VS{} else\VS{} y \ldots }}

   235 \end{center}

   236 

   237 \noindent

   238 The crucial idea of the algorithm is to build the derivative of all 

   239