--- a/progs/re-internal.rb Wed Oct 02 00:10:52 2013 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,22 +0,0 @@
-# provided by Daniel Baldwin
-
-nums = (1..100)
-
-#iterate through the nums 1-100
-nums.each do |i|
-
- start_time = Time.now
- string = "a" * i
-
- #create a new regular expression based on current value of i
- re = Regexp.new(/((a?){#{i}})(a{#{i}})/)
-
- re.match(string)
- #if re.match(string)
- # puts "matched string a * #{i} with regex #{re}"
- #else
- # puts "unmatched string a * #{i} with regex #{re}"
- #end
-
- puts "#{i} %.5f" % (Time.now - start_time)
-end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/re.rb Wed Oct 02 01:02:50 2013 +0100
@@ -0,0 +1,22 @@
+# provided by Daniel Baldwin
+
+nums = (1..100)
+
+#iterate through the nums 1-100
+nums.each do |i|
+
+ start_time = Time.now
+ string = "a" * i
+
+ #create a new regular expression based on current value of i
+ re = Regexp.new(/((a?){#{i}})(a{#{i}})/)
+
+ re.match(string)
+ #if re.match(string)
+ # puts "matched string a * #{i} with regex #{re}"
+ #else
+ # puts "unmatched string a * #{i} with regex #{re}"
+ #end
+
+ puts "#{i} %.5f" % (Time.now - start_time)
+end
--- a/progs/re2.scala Wed Oct 02 00:10:52 2013 +0100
+++ b/progs/re2.scala Wed Oct 02 01:02:50 2013 +0100
@@ -1,3 +1,4 @@
+import scala.language.implicitConversions
abstract class Rexp
--- a/progs/re3.scala Wed Oct 02 00:10:52 2013 +0100
+++ b/progs/re3.scala Wed Oct 02 01:02:50 2013 +0100
@@ -1,3 +1,4 @@
+import scala.language.implicitConversions
abstract class Rexp {
def simp : Rexp = this
@@ -98,7 +99,7 @@
}
-for (i <- 1 to 11001 by 500) {
+for (i <- 1 to 12001 by 500) {
println(i + " " + "%.5f".format(time_needed(1, matcher(EVIL(i), "a" * i))))
}
--- a/progs/re4.scala Wed Oct 02 00:10:52 2013 +0100
+++ b/progs/re4.scala Wed Oct 02 01:02:50 2013 +0100
@@ -1,4 +1,5 @@
import scala.annotation.tailrec
+
abstract class Rexp {
def simp : Rexp = this
}
@@ -12,7 +13,7 @@
case (r, NULL) => r
case (r, EMPTY) => if (nullable(r)) r else ALT(r, EMPTY)
case (EMPTY, r) => if (nullable(r)) r else ALT(r, EMPTY)
- case (r1, r2) => ALT(r1, r2)
+ case (r1, r2) => if (r1 == r2) r1 else ALT(r1, r2)
}
}
case class SEQ(r1: Rexp, r2: Rexp) extends Rexp {
@@ -24,8 +25,21 @@
case (r1, r2) => SEQ(r1, r2)
}
}
-case class STAR(r: Rexp) extends Rexp
-case class NTIMES(r: Rexp, n: Int) extends Rexp
+case class STAR(r: Rexp) extends Rexp {
+ override def simp = r.simp match {
+ case NULL => EMPTY
+ case EMPTY => EMPTY
+ case r => STAR(r)
+ }
+}
+case class NTIMES(r: Rexp, n: Int) extends Rexp {
+ override def simp = if (n == 0) EMPTY else
+ r.simp match {
+ case NULL => NULL
+ case EMPTY => EMPTY
+ case r => NTIMES(r, n)
+ }
+}
// some convenience for typing in regular expressions
def charlist2rexp(s : List[Char]) : Rexp = s match {
@@ -45,7 +59,7 @@
case ALT(r1, r2) => nullable(r1) || nullable(r2)
case SEQ(r1, r2) => nullable(r1) && nullable(r2)
case STAR(_) => true
- case NTIMES(r, i) => if (i == 0) false else nullable(r)
+ case NTIMES(r, i) => if (i == 0) true else nullable(r)
}
// derivative of a regular expression w.r.t. a character
@@ -73,18 +87,10 @@
def matcher(r: Rexp, s: String) : Boolean = nullable(ders(s.toList, r))
-
//one or zero
def OPT(r: Rexp) = ALT(r, EMPTY)
-//n-times
-/*def NTIMES(r: Rexp, n: Int) : Rexp = n match {
- case 0 => NULL
- case 1 => r
- case n => SEQ(r, NTIMES(r, n - 1))
-}*/
-
-def RTEST(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
+def EVIL(n: Int) = SEQ(NTIMES(OPT("a"), n), NTIMES("a", n))
def time_needed[T](i: Int, code: => T) = {
val start = System.nanoTime()
@@ -94,8 +100,8 @@
}
-for (i <- 1 to 13001 by 500) {
- println(i + " " + time_needed(1, matcher(RTEST(i), "a" * i)))
+for (i <- 1 to 12001 by 500) {
+ println(i + " " + "%.5f".format(time_needed(1, matcher(EVIL(i), "a" * i))))
}
Binary file slides/slides02.pdf has changed
--- a/slides/slides02.tex Wed Oct 02 00:10:52 2013 +0100
+++ b/slides/slides02.tex Wed Oct 02 01:02:50 2013 +0100
@@ -199,6 +199,36 @@
951 31.96038
\end{filecontents}
+\begin{filecontents}{re3.data}
+1 0.001605
+501 0.131066
+1001 0.057885
+1501 0.136875
+2001 0.176238
+2501 0.254363
+3001 0.37262
+3501 0.500946
+4001 0.638384
+4501 0.816605
+5001 1.00491
+5501 1.232505
+6001 1.525672
+6501 1.757502
+7001 2.092784
+7501 2.429224
+8001 2.803037
+8501 3.463045
+9001 3.609
+9501 4.081504
+10001 4.54569
+10501 6.17789
+11001 6.77242
+11501 7.95864
+\end{filecontents}
+
+
+
+
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -857,8 +887,6 @@
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[t]
@@ -913,15 +941,87 @@
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Examples\end{tabular}}
+
+Recall the example of \bl{$r \dn ((a \cdot b) + b)^*$} with
+
+\begin{center}
+\begin{tabular}{l}
+\bl{$der\,a\,r = ((\epsilon \cdot b) + \varnothing) \cdot r$}\\
+\bl{$der\,b\,r = ((\varnothing \cdot b) + \epsilon)\cdot r$}
+\end{tabular}
+\end{center}
+
+What are these regular expressions equal to?
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}\bl{$(a?\{n\}) \cdot a\{n\}$}\end{tabular}}
+
+\mbox{}\\[-9mm]
+
+\begin{tabular}{@ {\hspace{-5mm}}l}
+\begin{tikzpicture}[y=.2cm, x=.0008cm]
+ %axis
+ \draw (0,0) -- coordinate (x axis mid) (12000,0);
+ \draw (0,0) -- coordinate (y axis mid) (0,30);
+ %ticks
+ \foreach \x in {0,2000,...,12000}
+ \draw (\x,1pt) -- (\x,-3pt)
+ node[anchor=north] {\x};
+ \foreach \y in {0,5,...,30}
+ \draw (1pt,\y) -- (-3pt,\y)
+ node[anchor=east] {\y};
+ %labels
+ \node[below=0.6cm] at (x axis mid) {\bl{a}s};
+ \node[rotate=90, left=1.2cm] at (y axis mid) {secs};
+
+ %plots
+ \draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
+ file {re1.data};
+ \draw[color=green] plot[mark=square*, mark options={fill=white} ]
+ file {re2b.data};
+ \draw[color=black] plot[mark=square*, mark options={fill=white} ]
+ file {re3.data};
+
+ %legend
+ \begin{scope}[shift={(2000,20)}]
+ \draw[color=red] (0,0) --
+ plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (50,0)
+ node[right]{\small Scala V1};
+ \draw[yshift=13, color=green] (0,0) --
+ plot[mark=square*, mark options={fill=white}] (0.25,0) -- (50,0)
+ node[right]{\small Scala V2};
+ \draw[yshift=26, color=black] (0,0) --
+ plot[mark=square*, mark options={fill=white}] (0.25,0) -- (50,0)
+ node[right]{\small Scala V3};
+ \end{scope}
+\end{tikzpicture}
+\end{tabular}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\mode<presentation>{
\begin{frame}[c]
\frametitle{\begin{tabular}{c}Regular Languages\end{tabular}}
-A language (set of strings) is \alert{regular} iff there exists
-a regular expression that recognises all its strings.
+A language (a set of strings) is \alert{regular} iff there exists
+a regular expression that recognises all its strings.\bigskip\bigskip\pause
+
+Do you think there are languages that are {\bf not} regular?
\end{frame}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -947,20 +1047,6 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}The Rexp Matcher\end{tabular}}
-
-
-{\lstset{language=Scala}\fontsize{8}{10}\selectfont
-\texttt{\lstinputlisting{../progs/app7.scala}}}
-
-
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
\end{document}