afl-material: comparison videos/02-algo1.srt

equal deleted inserted replaced

-:34f77b976b88
+:f9686b22db7e
 Welcome back.
 Remember this slide.
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 00:00:09,700 --> 00:00:11,500
-This slide said, What is
+This slide said what is
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 00:00:11,500 --> 00:00:14,500
-all wreck expression Metro
+our regular expression matcher
 actually supposed to do?
 4
 00:00:14,500 --> 00:00:16,570
-It will take two arguments and
+It will take two arguments,
 5
 00:00:16,570 --> 00:00:18,670
-reg expression R and a string
+a regular expression r and a string s.
 6
 00:00:18,670 --> 00:00:21,580
-S. And it's supposed to say yes,
+And it's supposed to say yes,
 7
 00:00:21,580 --> 00:00:23,440
-the wreck expression matches
+the regular expression matches
 8
 00:00:23,440 --> 00:00:26,920
 the string if and only
 if the string is in
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 00:00:26,920 --> 00:00:28,855
-the language of R.
+the language of r.
 10
 00:00:28,855 --> 00:00:32,410
 And if the string is not
-in the language of our,
+in the language of r,
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 00:00:32,410 --> 00:00:35,515
 then our algorithm has to say no.
 this specification
 directly because remember,
 14
 00:00:39,565 --> 00:00:43,305
-this l Sometimes
+this L sometimes
 produces infinite sets.
 15
 00:00:43,305 --> 00:00:47,585
-And so we can test whether a
+And we can't test whether a
-string is an infinite set,
+string is in infinite set,
 16
 00:00:47,585 --> 00:00:50,090
 at least not easily.
 clever and implement
 some operations
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 00:00:57,050 --> 00:00:59,284
-on Rekha expressions instead.
+on regular expressions instead,
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 00:00:59,284 --> 00:01:03,275
-Because Weka expressions
+because regular expressions
 are always finite trees.
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 00:01:03,275 --> 00:01:05,870
 I should say the
 person who has been
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 00:01:05,870 --> 00:01:08,150
-clever is called brush-off ski.
+clever is called Brzozowski.
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 00:01:08,150 --> 00:01:11,435
-It's his, I've written,
+It's his algorithm
 I'm introducing here.
 25
 00:01:11,435 --> 00:01:15,515
 And his algorithm consists
 a regular expression as argument.
 28
 00:01:20,104 --> 00:01:24,155
 And the idea is that
-this function nullable.
+this function nullable is
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 00:01:24,155 --> 00:01:26,450
-Testing whether
+testing whether
-the reg expression
+the regular expression
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 00:01:26,450 --> 00:01:27,950
 can match the empty string.
 00:01:33,275 --> 00:01:35,465
 So that's defined as false.
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 00:01:35,465 --> 00:01:37,775
-This reg expression,
+This regular expression,
 the whole purpose
 35
 00:01:37,775 --> 00:01:39,680
 is that it can match
 00:01:39,680 --> 00:01:41,645
 So it's defined as true.
 37
 00:01:41,645 --> 00:01:44,599
-If a reg expression
+If a regular expression
 can match a character,
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 00:01:44,599 --> 00:01:47,045
 then it cannot match
 If an alternative can
 match the empty string,
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 00:01:53,180 --> 00:01:56,960
-then either or one can
+then either r1 can
-match the empty string.
+match the empty string,
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 00:01:56,960 --> 00:01:59,720
-Or R2 can match the empty string.
+or r2 can match the empty string.
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 00:01:59,720 --> 00:02:03,110
 So either nullable
-of R1 has to hold,
+of r1 has to hold,
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 00:02:03,110 --> 00:02:06,945
-or nullable of R2 has to hold.
+or nullable of r2 has to hold.
 45
 00:02:06,945 --> 00:02:09,925
 In this sequence, it's
 the other way around.
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 00:02:09,925 --> 00:02:12,790
-If this reg expression can
+If this regular expression can
 match the empty string,
 47
 00:02:12,790 --> 00:02:16,615
-then R1 has to be able to
+then r1 has to be able to
 match the empty string,
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 00:02:16,615 --> 00:02:20,290
-and R2 has to be able to
+and r2 has to be able to
 match the empty string.
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 00:02:20,290 --> 00:02:22,555
 So here it's just the opposite.
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 00:02:22,555 --> 00:02:25,660
-In one case it is o and
+In one case it is or and
-the other case it's end.
+the other case it is and.
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 00:02:25,660 --> 00:02:27,970
-In the store record
+The star regular
 expression can match
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 00:02:27,970 --> 00:02:30,445
 always the empty string.
 So this is a simple
 recursive function
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 00:02:33,340 --> 00:02:37,179
-and should not be too
+and it should not be too
 difficult to implement.
 55
 00:02:37,179 --> 00:02:42,025
 Okay, this nullable function
 If they have some problems
 with runtime, for example,
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 00:02:57,305 --> 00:02:58,940
-we can't expect that as
+we can't expect that
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 00:02:58,940 --> 00:03:03,260
-simple fix will solve all
+a simple fix will solve all
 the problems in the world.
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 00:03:03,260 --> 00:03:06,530
 So I admit the second
 that you understand it.
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 00:03:10,085 --> 00:03:12,140
 And it also just
-chose this preserves
+shows this Brzozowski
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 00:03:12,140 --> 00:03:14,345
-the is a very clever guy.
+is a very clever guy.
 66
 00:03:14,345 --> 00:03:15,800
 Actually, I have to say he was
 function is the following.
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 00:03:34,685 --> 00:03:38,120
 Imagine you have a
-reexpression and it can
+regular expression and it can
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 00:03:38,120 --> 00:03:41,930
 match a string of the
-form C followed by as.
+form c followed by s.
 75
 00:03:41,930 --> 00:03:44,810
-So the C is the first
+So the c is the first
 character of that string.
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 00:03:44,810 --> 00:03:48,605
-So I mentioned that can
+So I imagine that r can
 match this kind of string.
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 00:03:48,605 --> 00:03:50,330
 The question is now,
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 00:03:50,330 --> 00:03:52,400
-what would a wrecker
+what would a regular
 expression look
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 00:03:52,400 --> 00:03:54,695
-like that can match chest
+like that can match just
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 00:03:54,695 --> 00:03:57,140
 s. You probably remember
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 00:03:57,140 --> 00:03:59,300
 that from the semantic
-that every relative,
+derivative,
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 00:03:59,300 --> 00:04:00,860
 there was also
 something of chopping
 off the first character.
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 00:04:02,210 --> 00:04:04,940
 Here it's the same.
-If a reg expression
+If a regular expression
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 00:04:04,940 --> 00:04:07,835
 can match a string
-starting with a C,
+starting with a c,
 86
 00:04:07,835 --> 00:04:11,090
-we're looking for a wreck
+we're looking for a regular
 expression which can match
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 00:04:11,090 --> 00:04:15,215
 the rest of the string where
 And this operation will be called
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 00:04:17,690 --> 00:04:21,049
 the derivative of a
-wreck expression.
+regular expression.
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 00:04:21,049 --> 00:04:22,205
 And it will also take
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 00:04:22,205 --> 00:04:25,460
 a character as argument
-and the rec expression.
+and a regular expression.
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 00:04:25,460 --> 00:04:28,730
 And in contrast to
-the semantic records,
+the semantic
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 00:04:28,730 --> 00:04:31,310
-semantic derivative, which works
+derivative, which works
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 00:04:31,310 --> 00:04:34,430
 over languages or
-sets of strings.
+sets of strings,
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 00:04:34,430 --> 00:04:39,620
-This derivative works
+this derivative works
 over regular expressions.
 96
 00:04:39,620 --> 00:04:41,330
 Okay, here's this function.
 00:04:41,330 --> 00:04:43,970
 It's defined recursively over
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 00:04:43,970 --> 00:04:46,370
-the structure of rec expressions.
+the structure of regular expressions.
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 00:04:46,370 --> 00:04:48,814
 The first argument
 is the character,
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 00:04:48,814 --> 00:04:52,700
 and the second one is
-a wreck expression.
+a regular expression.
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 00:04:52,700 --> 00:04:56,510
 And remember the idea
 is we're looking for
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 00:04:56,510 --> 00:05:00,680
-a wreck expression that
+a regular expression that
-can match everything.
+can match everything
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 00:05:00,680 --> 00:05:03,125
-This reg expression
+this regular expression
 as argument can match
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 00:05:03,125 --> 00:05:07,040
-except for the C. So now let's
+except for the c. So now let's
 look at this first case.
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 00:05:07,040 --> 00:05:10,550
 So this reg expression
 So it certainly cannot
 match any string starting
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 00:05:14,270 --> 00:05:16,910
-a C. So we have to look
+a c. So we have to look
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 00:05:16,910 --> 00:05:20,090
-for and reg expression which
+for a regular expression which
-can not much anything.
+can not match anything.
 109
 00:05:20,090 --> 00:05:22,700
 Well, that's the purpose
-of this record expression,
+of this regular expression,
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 00:05:22,700 --> 00:05:24,815
 so we define it as 0.
 111
 00:05:24,815 --> 00:05:28,130
 In the next case,
-this reg expression
+this regular expression
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 00:05:28,130 --> 00:05:30,440
 can match the empty string,
 but it cannot match
 any string that starts
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 00:05:33,440 --> 00:05:36,350
-with C. So also in this case,
+with c. So also in this case,
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 00:05:36,350 --> 00:05:39,560
 we just define it as
-the bracket question,
+the regular expression,
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 00:05:39,560 --> 00:05:41,615
 which cannot match anything.
 117
 00:05:41,615 --> 00:05:45,170
 In the next case, this
-C as the argument to
+c is the argument to
 118
 00:05:45,170 --> 00:05:48,335
 the derivative and this d
-is the Rekha expression.
+is the regular expression.
 119
 00:05:48,335 --> 00:05:50,225
 So now there are two cases.
 120
 00:05:50,225 --> 00:05:53,525
-If this C and this D
+If this c and this d
-is actually equal.
+is actually equal,
 121
 00:05:53,525 --> 00:05:55,970
-That means this record
+Thaat means this regular
 expression can match
 122
 00:05:55,970 --> 00:05:59,240
-a string which just contains C0.
+a string which just contains c.
 123
 00:05:59,240 --> 00:06:01,505
 So if we strip that off,
 124
 00:06:01,505 --> 00:06:04,790
-motor remains is
+what remains is
 the empty string.
 125
 00:06:04,790 --> 00:06:06,890
 What is a regular expression
 match the empty string.
 127
 00:06:09,170 --> 00:06:11,915
 Well, that's the
-purpose of the warm.
+purpose of the 1.
 128
 00:06:11,915 --> 00:06:15,440
 And if c is not equal to d,
 129
 00:06:15,440 --> 00:06:17,630
-then this reg expression
+then this regular expression
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 00:06:17,630 --> 00:06:19,220
 cannot match anything
 which starts with
 131
 00:06:19,220 --> 00:06:23,780
-a C. So again it will
+a c. So again it will
 be defined as just 0.
 132
 00:06:23,780 --> 00:06:29,390
-Okay? Now, the alternative case,
+Now, the alternative case,
 133
 00:06:29,390 --> 00:06:31,970
-if this reg expression can
+if this regular expression can
 134
 00:06:31,970 --> 00:06:36,050
-match the strings
+match strings
-starting with C,
+starting with c,
 135
 00:06:36,050 --> 00:06:40,820
 then it can either be
-matched by the Ongwen.
+matched by the r1
 136
 00:06:40,820 --> 00:06:44,495
-Or it can be much by the R2.
+or it can be matched by the r2.
 137
 00:06:44,495 --> 00:06:50,090
-If they are one can match C
+If the r1 can match c
 and then following a string,
 138
 00:06:50,090 --> 00:06:53,975
 then we just have to recursively
 call the derivative for
 139
 00:06:53,975 --> 00:06:56,570
-R to get a reg expression
+r1 to get a regular expression
 140
 00:06:56,570 --> 00:06:59,135
 that can match the
 rest of the string.
 141
 00:06:59,135 --> 00:07:02,690
-And the same we can do with R2.
+And the same we can do with r2.
 142
 00:07:02,690 --> 00:07:06,110
-You can find a reg expression
+You can find a regular expression
-which can match everything.
+which can match everything
 143
 00:07:06,110 --> 00:07:07,850
-This R2 can match,
+this r2 can match,
 144
 00:07:07,850 --> 00:07:09,710
-starting with C, bad,
+starting with c, but
 145
 00:07:09,710 --> 00:07:12,590
-which chopping off this C. Okay?
+we are chopping off this c.
 146
 00:07:12,590 --> 00:07:16,370
 So now if you have to find
-the break expression,
+the regular expression,
 147
 00:07:16,370 --> 00:07:20,030
 which can match all the strings
-where C is tripped off.
+where c is chopped off,
 148
 00:07:20,030 --> 00:07:22,295
-Then we just have to
+then we just have to
-take the alternatives
+take the alternative
 149
 00:07:22,295 --> 00:07:24,965
 of these two derivatives.
 150
 00:07:24,965 --> 00:07:29,390
-Okay? Now to sequence case,
+Now to sequence case.
 151
 00:07:29,390 --> 00:07:33,005
-this sequence case is the
+This sequence case is the
 most complicated one.
 152
 00:07:33,005 --> 00:07:35,180
 And let's look first at
 153
 00:07:35,180 --> 00:07:39,335
-the second case where
+the second case, in the
-the Earth's brush.
+else branch.
 154
 00:07:39,335 --> 00:07:42,830
-Okay? So if this
+So if this
 regular expression
 155
 00:07:42,830 --> 00:07:46,145
 can match a string
-starting with C,
+starting with c,
 156
 00:07:46,145 --> 00:07:48,155
 then the following
 must have happened.
 157
 00:07:48,155 --> 00:07:51,905
-First, the R1 must have matched
+First, the r1 must have matched
-a string starting with C
+a string starting with c
 158
 00:07:51,905 --> 00:07:56,420
 and then anything coming
 afterwards with r2.
 159
 00:07:56,420 --> 00:07:59,660
-Okay? So in this case I only
+So in this case I only
 160
 00:07:59,660 --> 00:08:03,260
 have to call this
-derivative for this r one.
+derivative for this r1,
 161
 00:08:03,260 --> 00:08:06,830
-And find the reg expression
+and find the regular expression
 which can match everything
 162
 00:08:06,830 --> 00:08:11,555
-this R one can match except
+this r1 can match except
-for this C chopped off.
+for this c chopped off.
 163
 00:08:11,555 --> 00:08:15,830
-And I have to build that
+And I have to build the
 sequence derivative of that.
 164
 00:08:15,830 --> 00:08:18,260
-So that's what the As per se.
+So that's what the else branch says:
 165
 00:08:18,260 --> 00:08:21,860
-So I take the
+I take the
-derivative of R1 and I
+derivative of r1 and I
 166
 00:08:21,860 --> 00:08:23,480
-put the R2 on
+put the r2 on
 167
 00:08:23,480 --> 00:08:25,865
 the back because that's
 the rest of the string.
 168
 00:08:25,865 --> 00:08:29,240
-Ok? So that's the only
+So that's the only
 case we have to consider
 169
 00:08:29,240 --> 00:08:32,750
 this sequence case
-except if not the,
+except if not the
 170
 00:08:32,750 --> 00:08:37,895
-how one can match the
+r1 can match the
-sea and something else.
+c and something else.
 171
 00:08:37,895 --> 00:08:42,965
-But if on mismatching
+But if r1 is matching
-actually the empty string,
+actually the empty string.
 172
 00:08:42,965 --> 00:08:48,890
-this case actually the R two
+In this case actually the r2
 is in charge of matching
 173
 00:08:48,890 --> 00:08:51,590
-the string starting with C. So in
+the string starting with c. So in
 174
 00:08:51,590 --> 00:08:55,490
 this case we have to call
-the derivative for R2.
+the derivative for r2.
 175
 00:08:55,490 --> 00:08:57,875
 So that's why we have
 these two cases.
 176
 00:08:57,875 --> 00:09:00,455
-So if R1 is nullable,
+So if r1 is nullable,
 177
 00:09:00,455 --> 00:09:03,245
 then it can match
 the empty string.
 And we have to
 consider the case that
 179
 00:09:05,330 --> 00:09:08,045
-this R2 is matching a string
+this r2 is matching a string
 180
 00:09:08,045 --> 00:09:10,700
-starting with C. And so we have
+starting with c. And so we have
 181
 00:09:10,700 --> 00:09:14,210
 to call the derivative
-for this R2 in this case.
+for this r2 in this case.
 182
 00:09:14,210 --> 00:09:18,680
-Otherwise, the R1 will
+Otherwise, the r1 will
 be in charge of matching
 183
 00:09:18,680 --> 00:09:20,840
 a part of that
 string starting with
 184
 00:09:20,840 --> 00:09:24,695
-C. And I have to call the
+c. And I have to call the
-derivative on this R1.
+derivative on this r1.
 185
 00:09:24,695 --> 00:09:30,670
-Okay? I hope this makes sense.
+I hope this makes sense.
 186
 00:09:30,670 --> 00:09:34,150
 Go over that and
-also the handouts.
+also the handouts
 187
 00:09:34,150 --> 00:09:37,465
-Again. With that, that's
+again. That case
-it's really subtle.
+is really subtle.
 188
 00:09:37,465 --> 00:09:40,945
 And how do I remember this case?
 00:09:45,310 --> 00:09:48,160
 then I will always remember
 192
 00:09:48,160 --> 00:09:53,275
-the else branch where pushes
+the else branch where it pushes
-NG derivative over the R1.
+the derivative over the r1.
 193
 00:09:53,275 --> 00:09:55,780
-So are usually write
+So I usually write
-down the S punch
+down the else branch first,
 194
 00:09:55,780 --> 00:09:59,650
-first and then construct
+and then construct
-the thin branch by saying,
+the then branch by saying,
 195
 00:09:59,650 --> 00:10:01,525
 well, I just repeat this.
 in that case I
 197
 00:10:03,760 --> 00:10:06,580
 have to build also
-derivative of R2.
+derivative of r2.
 198
 00:10:06,580 --> 00:10:12,695
-Okay? Finally, the star case.
+Finally, the star case.
 199
 00:10:12,695 --> 00:10:15,665
-Ok. So here again
+So here again
 we're looking for
 200
 00:10:15,665 --> 00:10:17,300
-a reg expression which
+a regular expression which
 201
 00:10:17,300 --> 00:10:19,745
 can match the string
-starting with C,
+starting with c,
 202
 00:10:19,745 --> 00:10:22,355
 except that the c has
 been chopped off.
 203
 00:10:22,355 --> 00:10:28,640
-So if r star has to match
+So if r* has to match
-a string starting with C,
+a string starting with c,
 204
 00:10:28,640 --> 00:10:32,735
 then at least we need one
-copy of this r. Okay?
+copy of this r.
 205
 00:10:32,735 --> 00:10:34,310
 So at least one copy of
 this r has matched
 something which starts with
 207
 00:10:37,010 --> 00:10:38,870
-a C and then afterwards
+a c and then afterwards
 208
 00:10:38,870 --> 00:10:41,570
 come 0 more copies
-of this OnStar.
+of this r*.
 209
 00:10:41,570 --> 00:10:45,530
-Okay? What we do there
+What we do there
-is we trying to find
+is we are trying to find
 210
 00:10:45,530 --> 00:10:47,960
-the Rekha expression
+the regular expression
 which can match
 211
 00:10:47,960 --> 00:10:50,915
 this first part of the string.
 212
 00:10:50,915 --> 00:10:53,255
 However, where the
-sea is chopped off.
+c is chopped off.
 213
 00:10:53,255 --> 00:10:55,130
 And then we just say, well,
 00:10:57,050 --> 00:10:59,030
 0 or more copies of
 216
 00:10:59,030 --> 00:11:02,600
-this R. So that's why
+this r. So that's why
 it's defined like this.
 217
 00:11:02,600 --> 00:11:09,050
-Okay? S8. Please take care
+Okay? ...As said, please take care
 with this definition.
 218
 00:11:09,050 --> 00:11:11,435
 That's not so simple.
 different ways in
 the next slides.
 223
 00:11:20,825 --> 00:11:24,695
-Okay, let's look
+Let's look
-first some examples.
+first at some examples.
 224
 00:11:24,695 --> 00:11:27,140
 So here is a regular expression,
 225
 00:11:27,140 --> 00:11:29,390
-R. And let's have
+r. And let's have
 226
 00:11:29,390 --> 00:11:32,450
 a look at these three
 derivatives according to a,
 227
 00:11:32,450 --> 00:11:38,405
-B, and C. And Vishal do
+b, and c. And we shall do
-with d1 for the a. Ok.
+the one for a.
 228
 00:11:38,405 --> 00:11:42,379
-So here is our reg expression
+So here is our regular expression
 229
 00:11:42,379 --> 00:11:45,334
-and was very generous
+and I was very generous
-with dependent a thesis.
+with parentheses.
 230
 00:11:45,334 --> 00:11:48,140
 And the outermost is a star.
 231
 00:11:48,140 --> 00:11:52,550
-So if people now the
+So we now build the
 derivative according to a,
 232
 00:11:52,550 --> 00:11:55,474
-the character a of
+the character a, of
-that wreck expression.
+that regular expression.
 233
 00:11:55,474 --> 00:11:57,380
-Okay? So the first thing we
+So the first thing we
 234
 00:11:57,380 --> 00:11:59,555
-have to analyze is the K star.
+have to analyse is the case star.
 235
 00:11:59,555 --> 00:12:04,370
-Ok? So here's direct expression,
+So here's the regular expression,
 which we are looking at.
 236
 00:12:04,370 --> 00:12:09,170
-This are the outermost
+This r and the outermost
 constructor is this star.
 237
 00:12:09,170 --> 00:12:11,510
 If you go back to the definition,
 00:12:11,510 --> 00:12:13,625
 I hope you have it next to you,
 239
 00:12:13,625 --> 00:12:16,340
-then this star case is defined
+then this star-case is defined
 240
 00:12:16,340 --> 00:12:20,000
-as u taking just the
+as you're taking just the
 inside of the star
 241
 00:12:20,000 --> 00:12:23,030
 and apply this derivative and
 242
 00:12:23,030 --> 00:12:26,765
-leave the are on the
+leave the r on the
 outside at the end.
 243
 00:12:26,765 --> 00:12:29,990
 Ok. So that's the first step.
 Now we have to analyze
 245
 00:12:32,030 --> 00:12:36,035
 the derivative according to
-a of this record expression,
+a of this regular expression,
 246
 00:12:36,035 --> 00:12:38,000
 which is an alternative.
 we just have to push the
 derivative into each component,
 250
 00:12:45,185 --> 00:12:47,705
-into the a, followed by b.
+into the a followed by b.
 251
 00:12:47,705 --> 00:12:49,145
-And in this segment,
+And into the second
 252
 00:12:49,145 --> 00:12:51,185
-alternative into b. Ok,
+alternative, into b.
 253
 00:12:51,185 --> 00:12:56,030
-so we take the derivative
+We take the derivative
-of each according to a way.
+of each according to a.
 254
 00:12:56,030 --> 00:13:00,635
 Now this one is a sequence
-break expression.
+regular expression.
 255
 00:13:00,635 --> 00:13:02,210
-This most complicated case.
+This was the complicated case.
 256
 00:13:02,210 --> 00:13:04,160
-So the first of all
+First of all
-you have to test is,
+we have to test is
 257
 00:13:04,160 --> 00:13:07,910
-is the first component
+the first component
 nullable of this sequence?
 258
 00:13:07,910 --> 00:13:09,200
 Well, that is a,
 in this case, a on its
 own is not nullable.
 260
 00:13:12,740 --> 00:13:14,210
-So vn, the easy case,
+So we are the easy case,
 261
 00:13:14,210 --> 00:13:17,000
 we only have a single derivative
 00:13:27,920 --> 00:13:29,720
 And in this case the character
 266
 00:13:29,720 --> 00:13:31,715
-in the regular expression agree.
+and the regular expression agree.
 267
 00:13:31,715 --> 00:13:33,890
 So it's defined as one.
 00:13:33,890 --> 00:13:37,550
 Ok? In the other case,
 269
 00:13:37,550 --> 00:13:39,710
-the break expression is P,
+the regular expression is b,
 270
 00:13:39,710 --> 00:13:41,675
-But the characters a.
+but the characters a.
 271
 00:13:41,675 --> 00:13:46,385
 So in this case
 it's defined as 0.
 because originally we
 started with a star.
 275
 00:13:55,280 --> 00:13:58,295
-This expression is that
+This regular expression is that star.
-star at expression.
 276
 00:13:58,295 --> 00:14:02,780
-Ok? So the derivative
+So the derivative
 according to a
 277
 00:14:02,780 --> 00:14:07,610
-up that reg expression
+of that regular expression
 is this expression.
 278
 00:14:07,610 --> 00:14:10,970
 We just have to
-substitute this back in.
+substitute this r back in.
 279
 00:14:10,970 --> 00:14:13,745
 Just coming back to this slide.
 280
 00:14:13,745 --> 00:14:16,160
-So far, they're only analyze
+So far, we only analyzes
 281
 00:14:16,160 --> 00:14:19,505
 the derivative according
 to a single character.
 to the empty string,
 285
 00:14:27,905 --> 00:14:30,875
 we just return the
-Rekha expression.
+regular expression.
 286
 00:14:30,875 --> 00:14:35,585
 If we have a string
 starting with character c,
 287
 00:14:35,585 --> 00:14:37,850
 remember that can
-be any character.
+be any character,
 288
 00:14:37,850 --> 00:14:42,170
-Then we build first the simple
+then we build first the simple
 derivative according to
 289
 00:14:42,170 --> 00:14:44,360
 that first character and
 rest of the string.
 291
 00:14:46,925 --> 00:14:50,615
 So here you see again,
-my personal convention.
+my personal convention:
 292
 00:14:50,615 --> 00:14:54,365
-Everything which works on
+everything which works on
-lists has this S at the end.
+lists has this s at the end.
 293
 00:14:54,365 --> 00:14:57,125
 So this function is
 for single characters.
 state what the algorithm
 is, the complete algorithm.
 302
 00:15:20,600 --> 00:15:23,465
-So the pro shops ki mantra
+So the Brzozowski matcher
 303
 00:15:23,465 --> 00:15:24,860
 takes a regular expression as
 string as argument.
 305
 00:15:26,915 --> 00:15:30,920
 And is supposed to say yes if
-the reg expression matches
+the regular expression matches
 306
 00:15:30,920 --> 00:15:33,560
-the string or No
+the string or no
 307
 00:15:33,560 --> 00:15:36,065
-if the reg expression does
+if the regular expression does
 not match the string.
 308
 00:15:36,065 --> 00:15:37,715
 And how does it do that?
 309
 00:15:37,715 --> 00:15:42,560
 Well, it takes this string
-s And this reg expression,
+s and this regular expression,
 310
 00:15:42,560 --> 00:15:43,925
-and it first built
+and it first builds
 311
 00:15:43,925 --> 00:15:48,845
 successive derivatives until
-that string is exhaust that.
+that string is exhausted.
 312
 00:15:48,845 --> 00:15:52,115
-Okay? Then you have
+Then you have
 a final derivative,
 313
 00:15:52,115 --> 00:15:53,839
-a final reg expression.
+a final regular expression
 314
 00:15:53,839 --> 00:15:55,370
-And you test whether
+and you test whether
 315
 00:15:55,370 --> 00:15:57,920
-this reg expression can
+this regular expression can
 match the empty string.
 316
 00:15:57,920 --> 00:16:01,370
 If yes, then the
-original reg expression
+original regular expression,
 317
 00:16:01,370 --> 00:16:03,245
-is r can match the string.
+this r, can match the string.
 318
 00:16:03,245 --> 00:16:05,210
 If no, if it cannot match
 the final derivative
 with the empty string,
 320
 00:16:08,030 --> 00:16:10,280
-then know this
+then no this
-regular expression,
+regular expression r
 321
 00:16:10,280 --> 00:16:12,905
-R cannot match that string.
+cannot match that string.
 322
 00:16:12,905 --> 00:16:16,010
 I know it looks
 very anticlimactic,
 00:16:19,625 --> 00:16:22,760
 that it's not that complicated.
 325
 00:16:22,760 --> 00:16:25,340
-So how does the algorithm work?
+So how does the algorithm work
 326
 00:16:25,340 --> 00:16:27,634
-In a concrete example?
+in a concrete example?
 327
 00:16:27,634 --> 00:16:31,580
 Imagine you have a string, abc
 328
 00:16:31,580 --> 00:16:34,370
-and you have a break
+and you have a regular
-expression, say R1.
+expression, say r1.
 329
 00:16:34,370 --> 00:16:37,520
 And you want to find out
-whether this or one can match
+whether this r1 can match
 330
 00:16:37,520 --> 00:16:41,300
 that string abc or not.
 How do you do that?
 331
 00:16:41,300 --> 00:16:45,140
 Well, you would first
-take this R1 and you
+take this r1 and you
 332
 00:16:45,140 --> 00:16:47,150
 build the derivative according
 333
 00:16:47,150 --> 00:16:49,880
-to the first character, D-A.
+to the first character, the a.
 334
 00:16:49,880 --> 00:16:53,015
 Okay? You get the derivative,
 335
 00:16:53,015 --> 00:16:55,294
-which I call here R2.
+which I call here r2.
 336
 00:16:55,294 --> 00:16:58,640
 Then you take the next
-character, the B.
+character, the b.
 337
 00:16:58,640 --> 00:17:04,535
 You now build the derivative
-according to b of this R2.
+according to b of this r2.
 338
 00:17:04,535 --> 00:17:07,460
 Okay? So you take the
 result of the first step,
 second character.
 341
 00:17:11,810 --> 00:17:17,075
 Then you do this also with c.
-So you get a derivative R3,
+So you get a derivative r3,
 342
 00:17:17,075 --> 00:17:22,460
 and you build the derivative
-of R three according to c,
+of r3 according to c,
 343
 00:17:22,460 --> 00:17:24,185
-you get an R four.
+you get an r4.
 344
 00:17:24,185 --> 00:17:26,300
 Okay, so that's the
 final derivative.
 The string is exhausted.
 346
 00:17:27,530 --> 00:17:29,570
 We build derivatives
-according to a, B,
+according to a, b,
 347
 00:17:29,570 --> 00:17:34,610
-and C. Now we just test whether
+and c. Now we just test whether
-this r four is nullable.
+this r4 is nullable.
 348
 00:17:34,610 --> 00:17:37,175
 If it says yes,
 349
 00:17:37,175 --> 00:17:41,510
-then df break expression metro
+then the regular expression matcher
 will just say true, yes,
 350
 00:17:41,510 --> 00:17:43,340
-this original reg expression,
+this original regular expression,
 351
 00:17:43,340 --> 00:17:47,270
-the R1, will be able to
+the r1, will be able to
 match that string abc.
 352
 00:17:47,270 --> 00:17:50,585
 And if this test returns false,
 00:17:50,585 --> 00:17:53,015
 then the algorithm says false.
 354
 00:17:53,015 --> 00:17:56,975
-This reg expression will
+This regular expression will
 not match the string.
 355
 00:17:56,975 --> 00:18:00,260
-Ok, you might ask
+Ok, you might ask:
-why on earth does
+Why on earth does
 356
 00:18:00,260 --> 00:18:02,960
 that algorithm
-actually work away?
+actually work?
 357
 00:18:02,960 --> 00:18:06,515
-Here's an explanation
+Here's anather explanation
 for why it works.
 358
 00:18:06,515 --> 00:18:10,190
-Imagine you have a wreck
+Imagine you have a regular
-expression R1, okay?
+expression r1, okay?
 359
 00:18:10,190 --> 00:18:13,220
 And you have a string abc,
 00:18:13,220 --> 00:18:14,270
 and you want to find out
 361
 00:18:14,270 --> 00:18:17,180
-whether one can
+whether r1 can
 match that string.
 362
 00:18:17,180 --> 00:18:18,799
 And for the moment,
 00:18:22,610 --> 00:18:26,315
 Ok? So the language L of
 365
 00:18:26,315 --> 00:18:30,185
-R will actually
+r1 will actually
 contain that string,
 366
 00:18:30,185 --> 00:18:31,805
 otherwise it wouldn't match that.
 367
 00:18:31,805 --> 00:18:36,710
-Okay? So ABC is in
+Okay? So abc is in
 this language, okay?
 368
 00:18:36,710 --> 00:18:39,785
 If I now take the
 semantic derivative,
 369
 00:18:39,785 --> 00:18:43,145
 that means I look at all
-the strings in this f,
+the strings in this L(r1)
 370
 00:18:43,145 --> 00:18:46,820
-R1, and further out
+and filter out
 371
 00:18:46,820 --> 00:18:48,740
 all the ones which
 do not start with
 00:18:48,740 --> 00:18:51,260
 an a, I discharge them.
 373
 00:18:51,260 --> 00:18:54,545
-And I only look the one
+And I only look at the ones
 which start with an a.
 374
 00:18:54,545 --> 00:18:56,465
 And of those strings,
 I chop off this a.
 376
 00:18:58,475 --> 00:19:01,025
 So after this
-romantic derivative,
+semantic derivative,
 377
 00:19:01,025 --> 00:19:05,735
 this set of strings will
-contain just B and C.
+contain just bc.
 378
 00:19:05,735 --> 00:19:12,830
 Ok. Now if I build the next
 semantic derivative of that,
 then I would look at
 380
 00:19:14,345 --> 00:19:16,850
 all the strings which
-start with a P,
+start with a b,
 381
 00:19:16,850 --> 00:19:21,350
 and forget about everything
-else of the ones.
+else. Of the remaining ones
 382
 00:19:21,350 --> 00:19:27,905
-I know they start with B.
+I know they start with b.
-I just chop of the B. Ok.
+I just chop of the b. Ok.
 383
 00:19:27,905 --> 00:19:31,655
 So in this whole set here,
 semantic derivative
 387
 00:19:44,420 --> 00:19:47,300
 because I want to find out
-whether ABC is involved.
+whether abc is matched.
 388
 00:19:47,300 --> 00:19:50,540
 Okay? So now I look
 at all the strings in
 here and look at
 390
 00:19:52,820 --> 00:19:55,340
 them whether they start
-with a C. If yes,
+with a c. If yes,
 391
 00:19:55,340 --> 00:19:56,885
-I chop off the sea.
+I chop off the c.
 392
 00:19:56,885 --> 00:19:59,120
-And put in markets remaining.
+And put in what is remaining.
 393
 00:19:59,120 --> 00:20:00,425
 So in this case,
 if I have the string c
 395
 00:20:02,510 --> 00:20:04,550
 in this language and
-I chop off this,
+I chop off this c,
 396
 00:20:04,550 --> 00:20:07,700
-see what is remaining
+what is remaining
 is the empty string.
 397
 00:20:07,700 --> 00:20:09,695
 So we have to check of
 contains the empty string.
 399
 00:20:14,510 --> 00:20:18,800
 If yes, then the
-original R1 can match
+original r1 can match
 400
 00:20:18,800 --> 00:20:21,050
-this ABC because this ABC
+this abc because this abc
 401
 00:20:21,050 --> 00:20:24,119
 must have been in this language.
 402
 00:20:24,130 --> 00:20:28,565
 And if in the end there wasn't
-the empty string, then,
+the empty string, then
 403
 00:20:28,565 --> 00:20:33,575
-then this ABC Watson in
+this abs was not in
-this language of one.
+this language of r1.
 404
 00:20:33,575 --> 00:20:36,260
-And so the electron must have,
+And so the lexer must have,
 405
 00:20:36,260 --> 00:20:38,880
-or the metro must have failed.
+or the matcher must have failed.
 406
 00:20:39,040 --> 00:20:42,530
 The clever bit is that here
 So that's not really
 an algorithm.
 411
 00:20:55,730 --> 00:20:58,880
-Yeah, that's just
+That's just
-explaining the idea with
+explaining the idea.
 412
 00:20:58,880 --> 00:21:02,525
-preserves key
+What Brzozowski
 achieved was that he
 413
 00:21:02,525 --> 00:21:06,440
 now works with this derivative
-America expressions and
+regular expressions and
 414
 00:21:06,440 --> 00:21:10,715
 somehow imitates what
 happens on these languages.
 415
 00:21:10,715 --> 00:21:14,135
 Because remember if you
-have an wreck expression,
+have a regular expression,
 416
 00:21:14,135 --> 00:21:17,405
-are you want to test
+and you want to test
-whether can match APC,
+whether it can match abc,
 417
 00:21:17,405 --> 00:21:22,550
 then you take first
 derivative according to a.
 418
 00:21:22,550 --> 00:21:25,760
-So you will get a wreck
+So you will get a regular
 expression which can match b
 419
 00:21:25,760 --> 00:21:29,464
-and c If R could match abc.
+and c, if r could match abc.
 420
 00:21:29,464 --> 00:21:31,430
 So after the first derivative,
 421
 00:21:31,430 --> 00:21:33,620
-you will get a wreck expression
+you will get a regular expression
-which can match B and
+which can match b and
 422
 00:21:33,620 --> 00:21:37,070
-C. If you take the
+c. If you take the
 second derivative,
 423
 00:21:37,070 --> 00:21:41,225
-you will get a reexpression
+you will get a regular expression
 which can match c alone.
 424
 00:21:41,225 --> 00:21:44,180
 And if you take the
 00:21:44,180 --> 00:21:46,070
 then you will get
 426
 00:21:46,070 --> 00:21:48,260
-rec expression which hopefully
+a regular expression which hopefully
 427
 00:21:48,260 --> 00:21:49,715
 can match the empty string.
 428
 00:21:49,715 --> 00:21:53,780
 If it does, then this
-R can match the ABC.
+r can match the abc.
 429
 00:21:53,780 --> 00:21:55,655
 And if it doesn't, then
 430
 00:21:55,655 --> 00:21:58,680
-ABC couldn't be
+abc couldn't be
-matched by this on.
+matched by this r.
 431
 00:21:58,900 --> 00:22:02,990
 Okay, let's have a look
 how this pans out in code.
 432
 00:22:02,990 --> 00:22:06,050
-Here's defile RE1.
+Here's the file re1.sc.
 433
 00:22:06,050 --> 00:22:07,940
-It's also uploaded on Keith,
+It's also uploaded on KEATS,
 434
 00:22:07,940 --> 00:22:10,625
 so you can see exactly
 what I'm doing.
 435
 00:22:10,625 --> 00:22:13,970
-And actually I already saw
+And actually you already saw
 that file because I showed you
 436
 00:22:13,970 --> 00:22:15,710
-how my wreck expressions are
+how my regular expressions are
 437
 00:22:15,710 --> 00:22:17,960
-defined with the
+defined, with the
 abstract classes here.
 438
 00:22:17,960 --> 00:22:21,155
 And here, the six cases
-for 0-1 character,
+for 0, 1, character,
 439
 00:22:21,155 --> 00:22:23,540
-I turn a TIF in
+alternative,
 sequence and star.
 440
 00:22:23,540 --> 00:22:26,705
 Ok. So the first
 we just go through
 all these six cases
 445
 00:22:37,040 --> 00:22:38,900
-are serious defined as false.
+0 is defined as false.
 446
 00:22:38,900 --> 00:22:43,234
-One is defined as true
+One is defined as true.
-character for any character,
+Character, for any character,
 447
 00:22:43,234 --> 00:22:45,455
-this null return false.
+this nullable will return false.
 448
 00:22:45,455 --> 00:22:47,540
-The alternative is to find here,
+The alternative is defined here,
 449
 00:22:47,540 --> 00:22:50,000
 so that's the or in Scala.
 450
 00:22:50,000 --> 00:22:52,700
 And for the sequence,
-that's the end.
+that's the and.
 451
 00:22:52,700 --> 00:22:56,180
 And this star, no matter
-what the reg expression is,
+what the regular expression is,
 452
 00:22:56,180 --> 00:22:59,540
 it will always match the
 empty string, so true.
 453
 00:22:59,540 --> 00:23:02,225
-So nanobots, very easy.
+So nullable is very easy.
 454
 00:23:02,225 --> 00:23:07,430
 The derivative is also not
 so much more complicated.
 It takes two arguments,
 456
 00:23:08,974 --> 00:23:11,810
 a character and the
-rec expression,
+regular expression,
 457
 00:23:11,810 --> 00:23:14,405
-and returns a wreck expression.
+and returns a regular expression.
 458
 00:23:14,405 --> 00:23:16,340
 So now we just have to analyze
 459
 00:23:16,340 --> 00:23:18,890
-what's that reg
+what's that regular
 expression looks like.
 460
 00:23:18,890 --> 00:23:23,870
 If it's 0, we return
-01, we return 0.
+0; if it's 1 we return 0.
 461
 00:23:23,870 --> 00:23:26,990
-If the character is the
+If the character... If the
-wreck expressions character
+regular expressions character
 462
 00:23:26,990 --> 00:23:30,260
-d. We test whether it's
+d, we test whether it's
-equal to this character.
+equal to this character
 463
 00:23:30,260 --> 00:23:32,225
-We want to take the
+we want to take the
 derivative off.
 464
 00:23:32,225 --> 00:23:36,185
-If yes, return one, otherwise 0.
+If yes, return 1, otherwise 0.
 465
 00:23:36,185 --> 00:23:38,600
 The alternative which has pushed
 If it's not the have to push
 471
 00:23:49,040 --> 00:23:52,160
 the derivative over
-the first DR1.
+the first, the r1.
 472
 00:23:52,160 --> 00:23:56,135
-And otherwise if it is null
+And otherwise if it is nullable,
-above we have two cases.
+we have two cases.
 473
 00:23:56,135 --> 00:24:00,605
 Either you have to push
-it over the R1 or R2.
+it over the r1 or r2.
 474
 00:24:00,605 --> 00:24:03,860
 And a star case, this one.
 We just build the sequence
 of the derivative of
 476
 00:24:07,160 --> 00:24:11,600
-R1 and append the
+r1 and append the
-or as a sequence,
+r1 as a sequence,
 477
 00:24:11,600 --> 00:24:14,195
 put the star at the end.
 478
 00:24:14,195 --> 00:24:19,430
-Okay, so here's this
+Okay, so here's the
 function for strings.
 479
 00:24:19,430 --> 00:24:21,740
 So a list of characters.
 480
 00:24:21,740 --> 00:24:23,870
-This function takes N,
+This function takes an s,
 481
 00:24:23,870 --> 00:24:26,480
-S list of characters argument
+a list of characters as argument
-and a reg expression
+and a regular expression
 482
 00:24:26,480 --> 00:24:29,360
 as argument and returns
-a wreck expression.
+a regular expression.
 483
 00:24:29,360 --> 00:24:31,460
 And we just have to
 pattern match what
 If it's the empty list,
 486
 00:24:35,360 --> 00:24:38,030
 it just immediately
-return the R. If
+return the r. If
 487
 00:24:38,030 --> 00:24:42,020
 it's something of the
-form C followed by S,
+form c followed by s,
 488
 00:24:42,020 --> 00:24:45,050
 then we build first the
 derivative according
 489
 00:24:45,050 --> 00:24:48,345
-to a C. And then
+to c. And then
 the result of that,
 490
 00:24:48,345 --> 00:24:50,090
-people recursively call
+we recursively call
 491
 00:24:50,090 --> 00:24:53,675
 the derivative
 according to s. Okay?
 492
 00:24:53,675 --> 00:24:56,060
-And now the main mantra,
+And now the main matcher,
 493
 00:24:56,060 --> 00:24:59,360
-it takes a reg
+it takes a regular
 expression and takes
 494
 00:24:59,360 --> 00:25:02,870
 a string and returns a
 The only thing I have to do here
 497
 00:25:07,430 --> 00:25:09,410
 because I'm implementing
-it and scholar,
+it in Scala,
 498
 00:25:09,410 --> 00:25:15,064
 I have to coerce between strings
 and lists of characters.
 00:25:15,064 --> 00:25:16,580
 So he, I take first
 500
 00:25:16,580 --> 00:25:20,810
-the two list of the S that
+the toList of the s. That
 gives me a list of characters.
 501
 00:25:20,810 --> 00:25:23,135
 Then I build this derivative
 502
 00:25:23,135 --> 00:25:26,045
-is ds because I'm
+with the s, because I'm
 looking at strings.
 503
 00:25:26,045 --> 00:25:28,160
 And then at the end,
 504
 00:25:28,160 --> 00:25:33,050
-built-in nullable of
+built the nullable of
 the final derivative.
 505
 00:25:33,050 --> 00:25:37,310
 The beauty of all this
 what's the derivative
 according to a,
 515
 00:26:00,305 --> 00:26:02,720
-B, and C of this
+b, and c of this
-record expression.
+regular expression.
 516
 00:26:02,720 --> 00:26:07,040
 And I hope you didn't
 make any mistake.
 517
 00:26:07,040 --> 00:26:09,260
 Now of course we want
-to see whether B
+to see whether we
 518
 00:26:09,260 --> 00:26:11,390
 do any better with
-this algorithm.
+this algorithm...
 519
 00:26:11,390 --> 00:26:13,715
-Then Python and Ruby.
+than Python and Ruby.
 520
 00:26:13,715 --> 00:26:16,070
 And let's first have a
 look at this example.
 521
 00:26:16,070 --> 00:26:18,079
-So this reg expression.
+So this regular expression.
 522
 00:26:18,079 --> 00:26:19,880
 The problem is that in
 523
 00:26:19,880 --> 00:26:22,070
-our reg expression
+our regular expression
-metro so far we have
+matcher so far we have
 524
 00:26:22,070 --> 00:26:24,530
-the sequence right
+the sequence rregular
-expression where we
+expression, but we
 525
 00:26:24,530 --> 00:26:27,200
 don't have this optional
-wreck expression.
+regular expression.
 526
 00:26:27,200 --> 00:26:30,800
 And we don't have this n
-times Rekha expression,
+times regular expression,
 527
 00:26:30,800 --> 00:26:36,605
 but we can quickly implement
 that in our implementation.
 528
 00:26:36,605 --> 00:26:40,549
 So if you want to build the
-optional reg expression,
+optional regular expression,
 529
 00:26:40,549 --> 00:26:41,870
 which is defined here,
 a little function which
 takes a reg expression and
 531
 00:26:44,570 --> 00:26:47,360
-returns the alternative of R one.
+returns the alternative of r and 1.
 532
 00:26:47,360 --> 00:26:49,624
 So it essentially
 takes the definition
 533
 00:26:49,624 --> 00:26:53,240
-of optional R and
+of optional r and
 replaces it by that.
 534
 00:26:53,240 --> 00:26:56,150
-The end times what we
+The n-times what we
-essentially do it,
+essentially do there is
 535
 00:26:56,150 --> 00:27:01,535
-There's beaches built n
+we built n copies of this r. Ok?
-copies of this r. Ok?
 536
 00:27:01,535 --> 00:27:04,745
-So if this n times was 0,
+So if this n-times was 0,
 537
 00:27:04,745 --> 00:27:06,245
 we just return one.
 538
 00:27:06,245 --> 00:27:11,570
 If it's one, then we return
-just the reg expression.
+just the regular expression.
 539
 00:27:11,570 --> 00:27:15,575
-And if it's a, something
+And if it's something
 bigger than one,
 540
 00:27:15,575 --> 00:27:18,560
 then we just built the
 these copies and call
 542
 00:27:20,270 --> 00:27:22,925
 this function again
-with n minus one.
+with n - 1.
 543
 00:27:22,925 --> 00:27:26,330
-So we just now n copies of that.
+So we just build now n-copies of that.
 544
 00:27:26,330 --> 00:27:30,710
-Okay? Okay, so we can look
+Okay, so we can look
 at our first example.
 545
 00:27:30,710 --> 00:27:32,629
-This is the work expression,
+This is the regular expression,
 546
 00:27:32,629 --> 00:27:36,035
 and I call that here
-even rec expression1.
+evil regular expression1.
 547
 00:27:36,035 --> 00:27:37,670
 It doesn't look as beautiful
 if this can be improved.
 But here it is.
 551
 00:27:43,640 --> 00:27:45,724
-Here's the reg expression,
+Here's the regular expression,
 552
 00:27:45,724 --> 00:27:49,520
 and here's a little function
 which measures the time.
 00:27:49,520 --> 00:27:53,180
 And we can now start testing
 554
 00:27:53,180 --> 00:27:57,845
-this reg expression with
+this regular expression with
-strings of just containing A's.
+strings just containing a's.
 555
 00:27:57,845 --> 00:28:00,020
-And we first a bit cautious,
+And we are first a bit cautious,
 556
 00:28:00,020 --> 00:28:04,985
-be tested between 020
+we test it between 0 and 20,
-and be count by two.
+and we count by two.
 557
 00:28:04,985 --> 00:28:08,330
 And I actually will not
-start that with Scala,
+start that within Scala,
 558
 00:28:08,330 --> 00:28:12,965
-but actually the orbital online.
+but actually use Ammonite.
 559
 00:28:12,965 --> 00:28:15,305
 And that's out.
 560
 00:28:15,305 --> 00:28:17,269
-And that correlates.
+And that calculates
 561
 00:28:17,269 --> 00:28:20,675
-So for 18 days it's pretty fast.
+for 18 a's. It's pretty fast.
 562
 00:28:20,675 --> 00:28:24,815
 But for 20 it already
-needs to seconds.
+needs 2 seconds.
 563
 00:28:24,815 --> 00:28:28,265
 And you can see
 actually this jump from
 564
 00:28:28,265 --> 00:28:32,825
 18 to 20 in the runtime
-is prepared to.
+is pretty bad too.
 565
 00:28:32,825 --> 00:28:37,460
 And if we actually measure
 it more accurately,
 00:28:39,770 --> 00:28:41,255
 And what turns out,
 568
 00:28:41,255 --> 00:28:45,830
-we actually inverse as Python
+we are actually worse than Python
 and Ruby in this example.
 569
 00:28:45,830 --> 00:28:49,230
 So I guess that's a fail.

changeset 769	f9686b22db7e
parent 766	e8402d8ec8e6