33 legend entries={Python,Ruby}, |
33 legend entries={Python,Ruby}, |
34 legend pos=north west, |
34 legend pos=north west, |
35 legend cell align=left] |
35 legend cell align=left] |
36 \addplot[blue,mark=*, mark options={fill=white}] |
36 \addplot[blue,mark=*, mark options={fill=white}] |
37 table {re-python.data}; |
37 table {re-python.data}; |
38 \addplot[brown,mark=pentagon*, mark options={fill=white}] |
38 \addplot[brown,mark=triangle*, mark options={fill=white}] |
39 table {re-ruby.data}; |
39 table {re-ruby.data}; |
40 \end{axis} |
40 \end{axis} |
41 \end{tikzpicture} |
41 \end{tikzpicture} |
42 & |
42 & |
43 \begin{tikzpicture} |
43 \begin{tikzpicture} |
44 \begin{axis}[xlabel={\pcode{a}s},ylabel={time in secs}, |
44 \begin{axis}[xlabel={\pcode{a}s},ylabel={time in secs}, |
45 enlargelimits=false, |
45 enlargelimits=false, |
46 xtick={0,3000,...,12000}, |
46 xtick={0,3000,...,12000}, |
47 xmax=12000, |
47 xmax=12500, |
48 ymax=35, |
48 ymax=35, |
49 ytick={0,5,...,30}, |
49 ytick={0,5,...,30}, |
50 scaled ticks=false, |
50 scaled ticks=false, |
51 axis lines=left, |
51 axis lines=left, |
52 width=6.5cm, |
52 width=6.5cm, |
290 |
290 |
291 \[ |
291 \[ |
292 Der\,c\,A\;\dn\;\{s\,|\,c\!::\!s \in A\} |
292 Der\,c\,A\;\dn\;\{s\,|\,c\!::\!s \in A\} |
293 \] |
293 \] |
294 |
294 |
295 \noindent |
295 \noindent This operation essentially transforms a set of |
296 which essentially transforms a set of strings $A$ by filtering out all |
296 strings $A$ by filtering out all strings that do not start |
297 strings that do not start with $c$ and then strips off the $c$ from |
297 with $c$ and then strips off the $c$ from all the remaining |
298 all the remaining strings. For example suppose $A = \{f\!oo, bar, |
298 strings. For example suppose $A = \{f\!oo, bar, f\!rak\}$ then |
299 f\!rak\}$ then |
299 \[ Der\,f\,A = \{oo, rak\}\quad,\quad Der\,b\,A = \{ar\} \quad |
300 \[ |
300 \text{and} \quad Der\,a\,A = \varnothing \] |
301 Der\,f\,A = \{oo, rak\}\quad,\quad |
|
302 Der\,b\,A = \{ar\} \quad \text{and} \quad |
|
303 Der\,a\,A = \varnothing |
|
304 \] |
|
305 |
301 |
306 \noindent |
302 \noindent |
307 Note that in the last case $Der$ is empty, because no string in $A$ |
303 Note that in the last case $Der$ is empty, because no string in $A$ |
308 starts with $a$. With this operation we can state the following |
304 starts with $a$. With this operation we can state the following |
309 property about $der$: |
305 property about $der$: |