Aufgaben:Exercise 1.8: Synthetically Generated Texts - Revision history

Guenter at 12:07, 10 August 2021

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Guenter at 11:27, 23 June 2021

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Guenter at 11:23, 23 June 2021

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Guenter: Guenter moved page Aufgaben:Aufgabe 1.8: Synthetisch erzeugte Texte to Aufgaben:Exercise 1.8: Synthetically Generated Texts

2021-06-22T11:30:57Z

Guenter moved page Aufgabe 1.8: Synthetisch erzeugte Texte to Exercise 1.8: Synthetically Generated Texts

Guenter at 11:29, 22 June 2021

2021-06-22T11:29:59Z

← Older revision		Revision as of 12:07, 10 August 2021
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−	{{quiz-Header\|Buchseite=~~Informationstheorie und Quellencodierung~~/~~Natürliche wertdiskrete Nachrichtenquellen~~	+	{{quiz-Header\|Buchseite=Information_Theory/Natural_Discrete_Sources
	}}		}}

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 }}
-[[File:Inf_A_1_8_vers2.png|right|frame|Two synthetically generated text files]]
+[[File:EN_Inf_A_1_8.png|right|frame|Two synthetically generated text files]]
 With the Windows programme&nbsp; "Discrete-Value Information Theory"&nbsp; from the Chair of Communications Engineering at the TU Munich

@@ Line 120: / Line 120: @@
 *This suggests that&nbsp; "the"&nbsp; occurs more often than average in an English text and thus also in the synthetic&nbsp; $\text{File 1}$, as the following graph shows.
 *But&nbsp; "the"&nbsp; does not occur in isolation in all marks &nbsp; &#8658; &nbsp; immediately preceded and followed by a space.
-[[File:Inf_A_1_8e_vers2.png|right|frame|Occurrence of&nbsp; "der",&nbsp; "die"&nbsp; and&nbsp; "das"&nbsp; in the German text]]
+[[File:Inf_A_1_8e_vers2.png|right|frame|Occurrence of&nbsp; "der",&nbsp; "die",&nbsp; "das"&nbsp; in the German text]]

@@ Line 120: / Line 120: @@
 *This suggests that&nbsp; "the"&nbsp; occurs more often than average in an English text and thus also in the synthetic&nbsp; $\text{File 1}$, as the following graph shows.
 *But&nbsp; "the"&nbsp; does not occur in isolation in all marks &nbsp; &#8658; &nbsp; immediately preceded and followed by a space.
 [[File:Inf_A_1_8e_vers2.png|right|frame|Occurrence of&nbsp; "der",&nbsp; "die"&nbsp; and&nbsp; "das"&nbsp; in the German text]]
 '''(5)'''&nbsp; <u>All statements</u> are true:
 *After&nbsp; "de",&nbsp; "r"&nbsp; is indeed most likely&nbsp; $(32.8\%)$,&nbsp; followed by&nbsp; "n"&nbsp; $(28.5\%)$,&nbsp; "s"&nbsp; $(9.3\%)$&nbsp; and&nbsp; "m"&nbsp; $(9.7\%)$.
@@ Line 129: / Line 130: @@
-The graph shows&nbsp; $\text{File 2}$&nbsp; with all occurrences of&nbsp;  "der",&nbsp; "die"&nbsp; "das".
+The graph shows&nbsp; $\text{File 2}$&nbsp; with all occurrences of&nbsp;  "der",&nbsp; "die",&nbsp; "das".
 {{ML-Fuß}}

@@ Line 91: / Line 91: @@
 {{ML-Kopf}}
 '''(1)'''&nbsp; The correct solution is <u>suggestion 1</u>.
-*In&nbsp; $\text{file 1}$&nbsp; you can recognise many English words, in&nbsp; $\text{file 2}$&nbsp; many German words.
+*In&nbsp; $\text{File 1}$&nbsp; you can recognise many English words, in&nbsp; $\text{File 2}$&nbsp; many German words.
 *Neither text makes sense.
 '''(2)'''&nbsp; Correct is <u>suggestions 2</u>. The estimations of Shannon and Küpfmüller confirm our result:
-*The probability of a blank character in&nbsp; $\text{file 1}$&nbsp; (English)&nbsp; $19.8\%$.&nbsp;
+*The probability of a blank space&nbsp; "BS"&nbsp; in&nbsp; $\text{File 1}$&nbsp; (English)&nbsp; $19.8\%$.&nbsp;
-*So on average every&nbsp; $1/0.198 = 5.05$&ndash;th character is a space. &nbsp;
+*So on average every&nbsp; $1/0.198 = 5.05$&ndash;th character is&nbsp; "BS". &nbsp;
 *The average word length is therefore
 :$$L_{\rm M} = \frac{1}{0.198}-1 \approx 4.05\,{\rm characters}\hspace{0.05cm}.$$
-*Correspondingly, for&nbsp; $\text{file 2}$&nbsp; (German):
+*Correspondingly, for&nbsp; $\text{File 2}$&nbsp; (German):
 :$$L_{\rm M} = \frac{1}{0.176}-1 \approx 4.68\,{\rm characters}\hspace{0.05cm}.$$
@@ Line 107: / Line 107: @@
 '''(3)'''&nbsp; The <u>first three statements</u> are correct, but not statement&nbsp;  '''(4)''':
 *To determine the entropy approximation&nbsp; $H_k$&nbsp; ,&nbsp; $k$&ndash;tuples must be evaluated, for example, for&nbsp; $k = 3$&nbsp;  the triples &nbsp; "aaa",&nbsp;  "aab", &nbsp; ....
-*According to the generation rule "New character depends on the two predecessors",&nbsp; $H_1$,&nbsp; $H_2$&nbsp; and&nbsp; $H_3$&nbsp; of&nbsp; "TEMPLATE"&nbsp; and&nbsp; "SYNTHESIS"&nbsp; will match, but only approximately due to the finite file length.
+*According to the generation rule "New character depends on the two predecessors",&nbsp; $H_1$,&nbsp; $H_2$&nbsp; and&nbsp; $H_3$&nbsp; of&nbsp; "TEMPLATE"&nbsp; and&nbsp; "SYNTHESIS"&nbsp; will match, <br>but only approximately due to the finite file length.
-*In contrast, the&nbsp; $H_4$& approximations differ more strongly because the third predecessor is not taken into account during generation.
+*In contrast, the&nbsp; $H_4$&nbsp; approximations differ more strongly because the third predecessor is not taken into account during generation.
-*It is only known that&nbsp; "SYNTHESIS"&nbsp; $H_4 < H_3$&nbsp; must also apply with regard to
+*It is only known that&nbsp; $H_4 < H_3$&nbsp; must also apply with regard to "SYNTHESIS".
 '''(4)'''&nbsp; Only <u>statement 1</u> is correct here:
-*Nach einem Leerzeichen (Wortanfang) folgt "t" mit&nbsp; $17.8\%$, während am Wortende (vor einem Leerzeichen) "t" nur mit der Häufigkeit&nbsp; $<8.3\%$&nbsp; auftritt.
+[[File:Inf_A_1_8d_vers2.png|right|frame|Occurrence of "...the..." in the English text]]
+*After a&nbsp; "BS"&nbsp; (beginning of a word),&nbsp; "t" follows with&nbsp; $17.8\%$, while at the end of a word&nbsp; (before a space),&nbsp; "t"&nbsp; occurs only with the frequency&nbsp; $8.3\%$.
-*Insgesamt beträgt die Auftrittswahrscheinlichkeit von "t" über alle Positionen im Wort gemittelt&nbsp; $7.4\%$.
+*Overall, the probability of&nbsp;  "t"&nbsp; averaged over all positions in the word is&nbsp; $7.4\%$.
-*Als dritter Buchstaben nach Leerzeichen und "t" folgt "h" mit fast&nbsp; $82\%$&nbsp; und nach "th" ist "e" mit&nbsp; $62%$&nbsp; am wahrscheinlichsten.&nbsp;
+*The third letter after&nbsp; "BS"&nbsp; and&nbsp;  "t"&nbsp; is&nbsp; "h"&nbsp; with almost&nbsp; $82\%$&nbsp; and after&nbsp; "th",&nbsp;  "e"&nbsp; is most likeky with&nbsp; $62\%$.
-*Das lässt daraus schließen, dass "the" in einem englischen Text überdurchschnittlich oft vorkommt und damit auch in der synthetischen&nbsp; $\text{Datei 1}$, wie folgende Grafik zeigt. Aber nicht bei allen Markierungen tritt "the" isoliert auf &nbsp; &#8658; &nbsp; direkt vorher und nachher ein Leerzeichen.
+*This suggests that&nbsp; "the"&nbsp; occurs more often than average in an English text and thus also in the synthetic&nbsp; $\text{File 1}$, as the following graph shows.
+*But&nbsp; "the"&nbsp; does not occur in isolation in all marks &nbsp; &#8658; &nbsp; immediately preceded and followed by a space.
 <br clear=all>
-'''(5)'''&nbsp; <u>Alle Aussagen</u> treffen zu:
+[[File:Inf_A_1_8e_vers2.png|right|frame|Occurrence of&nbsp; "der",&nbsp; "die"&nbsp; and&nbsp; "das"&nbsp; in the German text]]
-*Nach "de" ist tatsächlich "r" am wahrscheinlichsten&nbsp; $(32.8\%)$,&nbsp; gefolgt von "n" $(28.5\%)$,&nbsp; "s"&nbsp; $(9.3\%)$&nbsp; und "m"&nbsp; $(9.7\%)$.
+'''(5)'''&nbsp; <u>All statements</u> are true:
-*Dafür verantwortlich könnten&nbsp; "der",&nbsp; "den",&nbsp; "des"&nbsp; und&nbsp; "dem"&nbsp; sein.
+*After&nbsp; "de",&nbsp; "r"&nbsp; is indeed most likely&nbsp; $(32.8\%)$,&nbsp; followed by&nbsp; "n"&nbsp; $(28.5\%)$,&nbsp; "s"&nbsp; $(9.3\%)$&nbsp; and&nbsp; "m"&nbsp; $(9.7\%)$.
-[[File:Inf_A_1_8e_vers2.png|right|frame|Auftreten von "der",  "die" und "das" im deutschen Text]]
+*This could be responsible for&nbsp; "der",&nbsp; "den",&nbsp; "des"&nbsp; und&nbsp; "dem".
-* Nach "da" folgt "s" mit größter Wahrscheinlichkeit: &nbsp;  $48.2\%$.
+* "da"&nbsp; is most likely followed by&nbsp; "s"&nbsp; $(48.2\%)$.
-* Nach "di" folgt "e" mit größter Wahrscheinlichkeit: &nbsp;  $78.7\%$.
+* After&nbsp; "di"&nbsp; follows&nbsp; "e"&nbsp; with the highest probability &nbsp; $(78.7\%)$.
 {{ML-Fuß}}

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 {Which templates were used for the text synthesis shown here??
 |type="()"}
-+ Die&nbsp; $\text{File 1}$&nbsp; (red) is based on an English template.
++ $\text{File 1}$&nbsp; (red) is based on an English template.
-- Die&nbsp; $\text{File 1}$&nbsp; (red) is based on a German template.
+- $\text{File 1}$&nbsp; (red) is based on a German template.
-{Compare the mean word lengths of&nbsp; $\text{File 1}$&nbsp; and&nbsp; $\text{File 2}$&nbsp;.
+{Compare the mean word lengths of&nbsp; $\text{File 1}$&nbsp; and&nbsp; $\text{File 2}$.
 |type="[]"}
-- The words of the "English" file are longer on average.
+- The words of the&nbsp; "English"&nbsp; file are longer on average.
-+ The words of the "German" file are longer on average.
++ The words of the&nbsp; "German"&nbsp; file are longer on average.
@@ Line 72: / Line 72: @@
-{Which statements are true for the "English" text?
+{Which statements are true for the&nbsp; "English"&nbsp; text?
 |type="[]"}
 + Most words begin with&nbsp; "t".
@@ Line 78: / Line 78: @@
-{Which statements could be true for German texts?
+{Which statements could be true forthe&nbsp; "German"&nbsp; texts?
 |type="[]"}
-+ After&nbsp; "de"&nbsp; ist&nbsp; "r"&nbsp; is most likely.
++ After&nbsp; "de",&nbsp;  "r"&nbsp; is most likely.
-+ After&nbsp; "da"&nbsp; ist&nbsp; "s"&nbsp; is most likely.
++ After&nbsp; "da",&nbsp; "s"&nbsp; is most likely.
-+ After&nbsp; "di"&nbsp; ist&nbsp; "e"&nbsp; is most likely.
++ After&nbsp; "di",&nbsp; "e"&nbsp; is most likely.

@@ Line 46: / Line 46: @@
 ''Hints:''
 *The exercise belongs to the chapter&nbsp; [[Information_Theory/Natural_Discrete_Sources|Natural Discrete Sources]].
-*Reference is also made to the page&nbsp; [[Information_Theory/Natürliche_wertdiskrete_Nachrichtenquellen#Synthetisch_erzeugte_Texte|Synthetically Generated Texts]].
+*Reference is also made to the page&nbsp; [[Information_Theory/Natural_Discrete_Sources#Synthetically_generated_texts|Synthetically Generated Texts]].

@@ Line 5: / Line 5: @@
 [[File:Inf_A_1_8_vers2.png|right|frame|Two synthetically generated text files]]
-The former practical course attempt&nbsp; [http://en.lntwww.de/downloads/Sonstiges/Texte/Wertdiskrete_Informationstheorie.pdf Value Discrete Information Theory]&nbsp; by Günter Söder at the Chair of Communications Engineering at the TU Munich uses the Windows programme&nbsp; [http://en.lntwww.de/downloads/Sonstiges/Programme/WDIT.zip WDIT].&nbsp; The links given here lead to the PDF version of the practical course instructions or to the ZIP version of the programme.
+With the Windows programme&nbsp; "Discrete-Value Information Theory"&nbsp; from the Chair of Communications Engineering at the TU Munich
-With this programme
+*one can determine the frequencies of character triplets such as&nbsp; "aaa",&nbsp; "aab", ... ,&nbsp; "xyz", ...&nbsp; from a given text file&nbsp; "TEMPLATE"&nbsp; and save them in an auxiliary file,
+Starting with the German and English Bible translations, we have thus synthesised two files, which are indicated in the graphic:
-Starting with the German and English Bible translations, we have thus synthesised two files, which are indicated in the diagram:
+* $\text{File 1}$&nbsp; (red border),
-* die&nbsp; $\text{File 1}$&nbsp; (red border),
+* $\text{File 2}$&nbsp; (green border).
 It is not indicated which file comes from which template.&nbsp; Determining this is your first task.
-The two templates are based on the natural alphabet&nbsp; $(26$ letters$)$&nbsp; and the space&nbsp; ("LZ") &nbsp; &#8658; &nbsp; $M = 27$.&nbsp; In the German Bible, the umlauts have been replaced, for example "ä" &nbsp; &#8658; &nbsp; "ae".
+The two templates are based on the natural alphabet&nbsp; $(26$&nbsp; letters$)$&nbsp; and the "Blank Space"&nbsp; ("BS") &nbsp; &#8658; &nbsp; $M = 27$.&nbsp; In the German Bible, the umlauts have been replaced, for example "ä" &nbsp; &#8658; &nbsp; "ae".
 &nbsp; $\text{File 1}$&nbsp; has the following characteristics:
-* The most frequent characters are "LZ" with&nbsp; $19.8\%$, followed by "e" with&nbsp; $10.2\%$&nbsp; and "a" with&nbsp; $8.5\%$.
+* The most frequent characters are&nbsp;  "BS"&nbsp;  with&nbsp; $19.8\%$, followed by&nbsp;  "e"&nbsp;  with&nbsp; $10.2\%$&nbsp; and&nbsp;  "a"&nbsp;  with&nbsp; $8.5\%$.
-* After "LZ" (space), "t" occurs most frequently with&nbsp; $17.8\%$&nbsp;.
+* After&nbsp;  "BS",&nbsp;  "t"&nbsp;  occurs most frequently with&nbsp; $17.8\%$.
-* Before a space, "d" is most likely.
+* Before&nbsp;  "BS",&nbsp; "d"&nbsp; is most likely.
-* The entropy approximations in each case with the unit "bit/character" were determined as follows:
+* The entropy approximations in each case with the unit&nbsp; "bit/character"&nbsp; were determined as follows:
 :$$H_0 = 4.76\hspace{0.05cm},\hspace{0.2cm}
 H_1 = 4.00\hspace{0.05cm},\hspace{0.2cm}
@@ Line 34: / Line 32: @@
 H_4 = 2.81\hspace{0.05cm}.  $$
-In contrast, the analysis of&nbsp; $\text{file 2}$:
+In contrast, the analysis of&nbsp; $\text{File 2}$:
-* The most frequent characters are "LZ" with&nbsp; $17.6\%$&nbsp; followed by "e" with&nbsp; $14.4\%$&nbsp; and "n" with&nbsp; $8.9\%$.
+* The most frequent characters are&nbsp;  "BS"&nbsp; with&nbsp; $17.6\%$&nbsp; followed by&nbsp; "e"&nbsp; with&nbsp; $14.4\%$&nbsp; and&nbsp; "n"&nbsp; with&nbsp; $8.9\%$.
-* After "LZ", "d" is the most likely&nbsp; $(15.1\%)$&nbsp; followed by "s" with&nbsp; $10.8\%$.
+* After&nbsp;  "BS",&nbsp; "d"&nbsp; is most likely&nbsp; $(15.1\%)$&nbsp; followed by&nbsp; "s"&nbsp; with&nbsp; $10.8\%$.
-* After "LZ" and "d", the vowels "e"&nbsp; $(48.3\%)$,&nbsp; "i" $(23\%)$&nbsp; and "a"&nbsp; $(20.2\%)$&nbsp; are dominant.
+* After&nbsp;  "BS"&nbsp; and&nbsp; "d",&nbsp; the vowels&nbsp; "e"&nbsp; $(48.3\%)$,&nbsp; "i"&nbsp; $(23\%)$&nbsp; and&nbsp; "a"&nbsp; $(20.2\%)$&nbsp; are dominant.
-* The entropy approximations differ only slightly from those of&nbsp; $\text{file 1}$.
+* The entropy approximations differ only slightly from those of&nbsp; $\text{File 1}$.
 * For larger&nbsp; $k$&ndash;values, these are slightly larger, for example&nbsp; $H_3 = 3.17$&nbsp; instead of&nbsp; $H_3 = 3.11$.
@@ Line 47: / Line 45: @@
 ''Hints:''
-*The task belongs to the chapter&nbsp; [[Information_Theory/Natürliche_wertdiskrete_Nachrichtenquellen|Natural discrete value message sources]].
+*The exercise belongs to the chapter&nbsp; [[Information_Theory/Natural_Discrete_Sources|Natural Discrete Sources]].
+*Reference is also made to the page&nbsp; [[Information_Theory/Natürliche_wertdiskrete_Nachrichtenquellen#Synthetisch_erzeugte_Texte|Synthetically Generated Texts]].

← Older revision	Revision as of 11:30, 22 June 2021
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−	[[Category:Information Theory: Exercises\|^1.3 ~~Natürliche Nachrichtenquellen~~^]]	+	[[Category:Information Theory: Exercises\|^1.3 Natural Discrete Sources^]]