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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>ORCID:</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Viktor Shynkarenko and Inna Demidovich</article-title>
      </title-group>
      <contrib-group>
        <aff id="aff0">
          <label>0</label>
          <institution>Ukrainian State University of Science and Technologies</institution>
          ,
          <addr-line>2, аcademician Lazaryan str., Dnipro, 49010</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0001</lpage>
      <abstract>
        <p>Natural Language Texts Authorship Establishing was carried out on the basis of the hypothesis that each author has a peculiar the sentences structure forming style with different parts of speech. A natural language text was translated into a formal language generated by a formal stochastic grammar. For each product of the training sample, the corresponding stochastic formal grammar was restored. This method made it possible to reflect the author characteristic style in sentences building. On the basis of works statistical sample, inference rules and a probabilistic measure of their application were formed. The effectiveness of the proposed method was evaluated experimentally. In authorship establishing a probabilistic measure of the text belonging to a formal stochastic grammar was determined. To assess the reliability of the obtained results, the confidence interval of the probability measure was calculated. In the studies with the control sample, the possibility of the correct text authorship establishment is natural language texts, statistic analysis, text structure, text authorship, classification, parsing, confidence interval, formal stochastic grammar This article solves the problem of the text authorship determining by analyzing the sentences structure. It is important to note that the task of the texts authorship establishing, as well as the task of its attribution, is still relevant for today and covers a wide range of goals in various fields and is interesting to a number of specialists in various fields.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>2022 Copyright for this paper by its authors.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Related works</title>
      <p>
        Syntactic analysis of various text parts is a popular method for analyzing the author's work, its
semantics, focus and main idea of the work. However, this type of various directions texts analysis is
faced with the complexity of the syntactic model’s automatic formation [
        <xref ref-type="bibr" rid="ref4 ref5 ref6">4, 5, 6</xref>
        ]. This is largely due to
the complexity of the language structure itself, the variability of the word forms used and the very
sentences structure. Despite this, method of text research like this carries the greatest amount of
information about the author's style: regardless of the text subject, the syntactic structure of the author's
language will clearly display his syllable.
      </p>
      <p>
        Various studies of natural language formalization are known [
        <xref ref-type="bibr" rid="ref7 ref8">7, 8</xref>
        ]. One of the methods to work with
natural language is using of grammars [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. For example, similar studies were carried out for Italian [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]
and Ukrainian [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>
        Unlike the problem of text categorization, the goal of which is to determine a topic or list of topics
for a text based on its content, text parsing abstracts from a specific area and tries to understand
contentindependent features of a text that are "linguistic expressions" of individual authors [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. Such
contentindependent text properties are usually called stylometric features. For these purposes, various methods
have been proposed and applied in problems of authorship attribution, including: frequency of words
[
        <xref ref-type="bibr" rid="ref12 ref13">12, 13</xref>
        ], symbolic n-grams [
        <xref ref-type="bibr" rid="ref14 ref15 ref16">14, 15, 16</xref>
        ], auxiliary words, syllables [17] and parts of speech definition
[18, 19].
      </p>
      <p>
        The idea of using information about parts of speech is not new and has been successfully applied in
a number of style classification problems, where, in particular, texts in English were processed [
        <xref ref-type="bibr" rid="ref2">19, 2</xref>
        ].
As a rule, their repeating sequences were extracted on the parts of speech basis.
      </p>
      <p>The described approach is feasible for English texts, since the structure of the English language is
quite strict and the word order in a sentence is clearly assigned to a certain part of speech. In addition,
the words themselves do not have many different word forms, and when a prefix or suffix is added or
removed, they go into another part of speech category. However, with using such method into Ukrainian,
difficulties may arise. Unlike English, Ukrainian is a more variable language, and the number of forms
for one word due to case, gender, and number changing significantly complicates the task. Moreover,
the assignment of a word to one or another part of speech is ambiguous and difficult to perform within
the automatic process.</p>
      <p>The problem associated with establishing authorship need an individual approach in each case [20].
As a general rule, problems where the number of potential authors is small and the data samples are
large are considered easy and high accuracy is expected. Complexity increases with an increase in the
number of authors and a decrease in data volumes [21], which leads to a decrease in recognition
accuracy.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Methods</title>
    </sec>
    <sec id="sec-4">
      <title>3.1. Work structure rules formation</title>
      <p>This paper explores a method for the texts authorship determining based on the sentence structure
of the author's individual language.</p>
      <p>Stochastic grammar is used to create rules that describe the structure of sentences in a text. For each
rule, the probability of its application in a particular work is determined. The probability of inferring
the whole sentence is defined as the product of the parts of speech sequences probabilities used in it.
The resulting rules will generate a language that is specific for the explored and structurally similar
works of a certain author.</p>
      <p>To describe the main text structure, the parts of speech as a word characteristic were used. Thus,
each word in the sentence is replaced by the part of speech that it is.</p>
      <p>Each of the words in the text was analyzed for similarity with the parts of speech existing in the
Ukrainian language. For service parts of speech: prepositions, pronouns, conjunctions and interjections,
their list was used in all possible forms, and verbs, nouns, adverbs, adjectives, participles and participles
were determined by comparison with the list of word endings.</p>
      <p>When a corresponding word or its ending was found in one of the lists, the word was automatically
replaced with the corresponding part of speech. If it was not possible to automatically determine the
answer, the user was asked to then include the entire word or its ending (the data was entered manually
by the user) in an already existing list.</p>
      <p>The following tags were used to tag words in the text in Ukrainian: verb (v), noun (n), pronoun (prn),
adjective (adj), conjunction (cnj), adverb (adv), preposition (prp), participle (prtcpl), interjection (intrj),
gerund (ger).</p>
      <p>For each part of speech, the probability of its occurrence in a certain place of the sentence in the
given text is calculated. The probability of the certain part of speech appearance in the studied sequence
will allow us to more accurately capture the individual writing style specific of each of the authors
under study. After receiving the text in the form of parts of speech sequences set in sentences with the
probability of their occurrence in a particular place, rules are formed.</p>
      <p>To do this, all sentences starting with the same part of speech are grouped, the first word is discarded,
and the procedure for calculating the probability is repeated for the next word.</p>
      <p>After the sentences are again grouped according to the parts of speech at the beginning, the first
word is again discarded and the probability for the next element is calculated, and so on. Probability is
calculated as the number of cases in the text divided by their total number.
corresponding to the i-th rule applied when parsing the sentence or the i-th level of the rule),   , – j-th
non-terminal in the i-th level rule, pi,k – the probability of applying the corresponding rule when parsing
this work, Ji, Kt – is the number of different non-terminals in the right part of the rules of the i-1-th
level and i-th level, respectively.</p>
      <p>The level corresponds to the ordinal number of the word in the sentence. Several alternative rules are
allowed with a non-terminal on the left side of the rule, but the terminals on the right side of such rules
are different, which ensures deterministic parsing. Thus, the text is presented as a set of rules that describe
its structural features using the rules described above. The symbol ε stands for empty (end of rule).</p>
      <p>An example of the one automatically restored set of rules is presented below in Table 1. The rule
describes all 24 sentences in the text "Etude" by I. Bahrianyi, with a verb in the beginning. As can be
seen from the presented probabilities, in the studied work, 31% of sentences will begin with a verb.
And the percentage of sentences consisting of only one word, a verb, is 17%.</p>
      <p>Examples of the first few rules according to the table   1,1;
0,17 0,13
 1,1 →  ;  1,1 →   2,1 . On the left side of the rule is a non-terminal, then the probability of its
application is indicated, and on the right side of the rule is a terminal with a non-terminal to go to the next
rule.</p>
      <p>When using this text method, a sentence from the work "Etude" by I. Bahrianyi presented as a
sequence of parts of speech included in it will have the following form Table 2.</p>
    </sec>
    <sec id="sec-5">
      <title>3.2. Comparison of two works</title>
      <p>To compare two works, they must be presented in the form of a restored formal stochastic grammar
with the rules, the formation of which is described above. Each sequence of rules in one text is compared
with each sequence of rules in another text. Let the rules for some text Ti be formed like:
 ' →p'1j b'1 j A'1, j , A'i, j p→'i+1,k b'i+1,k A'i+1,k , j = 1 J 'i , k = 1 K 'i .</p>
      <p>Let's say in texts Ti and Tk there are sentences of similar structure, such as
pljl
bljl
in any of these works, if the text T2 structurally similar sentence to sentence Si is absent, then
 (Si , Si' ) = 0 .</p>
      <p>notice, that  (Ti ,Tk ) =  (Tk ,Ti )  (Ti ,Ti ) = 1 complete match,  (Ti ,Tk ) = 0 – if in texts Ti and Tk no
sentences have the same structure.</p>
      <p>Formation of formal stochastic grammars was carried out for all the works of each author in the
training sample, generating the language specific for a particular author. For determining the similarity of
a work according to (1), the formal stochastic grammar corresponding to the work from the control sample
was used as T1, and the stochastic grammar for all works of the potential author altogether was used as T2.</p>
    </sec>
    <sec id="sec-6">
      <title>3.3. Calculation of the confidence interval boundary values using Student's t-test</title>
      <p>To obtain more reliable results, we calculated confidence intervals for each of the authors in the
sample. Student's t-test was applied [22].</p>
      <p>To calculate the confidence interval in the training sample for each of the authors, their presented
texts similarities to each other were calculated. Data on the similarity of texts within the training sample
for each of the authors was divided into three parts with the same number of components.</p>
      <p>The following formula was used to calculate the confidence interval:</p>
      <p>2, √61 ∑3=1(ζ −   )2,
where t2,β – Student's t-test, β – confidence level, ζk – the average value of k-th sample part, θS – the
average value over the entire sample.</p>
    </sec>
    <sec id="sec-7">
      <title>4. Results</title>
    </sec>
    <sec id="sec-8">
      <title>4.1. Training and control samples formation</title>
      <p>During the experiment, the authorship of natural language texts was determined by two samples.</p>
      <p>For the first experiment, 20 works of literary texts by 10 Ukrainian authors were selected in the
training sample. The control sample consists of 3 works by each author.</p>
      <p>The works of the following authors are presented: IB – I. Bahrianyi, AV – A. Vyshnia, MV – M.
Vovchok, AD – A. Dovzhenko, HK – H. Kvitka-Osnovianenko, PM – P. Myrnyi, VN – V. Nestaiko,
VP – V. Pidmohylnyi, IF – I. Franko, MK – M. Khvylovyi.</p>
      <p>For the second experiment, both samples were doubled, respectively, the training sample included
40 works by the same authors, and 60 texts made up a new control sample - 6 works by each author.</p>
      <p>The choice of literary texts is due to the availability of reliable information about the works
authorship and the presence of each author specific style.</p>
    </sec>
    <sec id="sec-9">
      <title>4.2. Experiment results</title>
      <p>At Figure 1 and Figure 2 the results of the experiments are presented. Each bar in the chart represents
the works of a particular author from the control sample. The column is divided into two zones, where
the blue part displays the number of texts with correctly identified authorship, and the orange part shows
the number of texts with erroneous ones.
IB</p>
      <p>AV</p>
      <p>MV</p>
      <p>AD</p>
      <p>HK
True</p>
      <p>PM
False</p>
      <p>VN</p>
      <p>VP</p>
      <p>IF</p>
      <p>MKH</p>
      <p>According to the results obtained, working with the smaller of the two samples, containing a total
of 200 works by 10 authors in the training sample (20 for each author), and 30 works in the control
sample, cases of authorship correct attribution is 24, which is 80%.</p>
      <p>The best result was obtained working with the works of A. Dovzhenko, P. Myrnyi, V. Nestaiko and
V. Pidmohylnyi. I. Franko turned out to be the author with the most difficult to define style.</p>
      <p>Sample 40x6
IB</p>
      <p>AV</p>
      <p>MV</p>
      <p>AD</p>
      <p>VN</p>
      <p>VP</p>
      <p>IF</p>
      <p>MKH
HK
True</p>
      <p>PM
False</p>
      <p>According to theobtained results, working with a larger doubled sample (400 texts of 10 authors in
the training sample and 60 works in the control sample), the number of correctly determined cases is
45, which is 75%.</p>
      <p>The best result was obtained working with the works of P. Myrny. The authors of the most difficult
cases to detect are H. Kvitka-Osnovianenko and M. Vovchok - the athurship of only a half of their
works in the sample was correctly determined.</p>
      <p>To obtain better result, a confidence interval was introduced Table 3.</p>
      <p>Confidence intervals of different authors differ significantly from each other. So, on average, the
interval ranges from 0.04 to 0.08, however, for A. Vyshnia and M. Vovchok it is much larger, and
amounted to 0.37 and 0.12, respectively. The minimum interval was 0.02 for V. Pidmohylnyi.</p>
      <p>For some of the authors, such as H. Kvitka-Osnovianenko and M. Vovchok, a special style of
narration is characteristic, which is difficult to classify and structure, due to which they are characterized
by a low recognition result.</p>
      <p>Whereas the authors I. Bahrianyi, A. Vyshnia, A. Dovzhenko, P. Myrnbi and V. Nestaiko have a
more individual style of writing, which is displayed in the sentence structure and allows establishing
their authorship with high accuracy.</p>
      <p>According to the results obtained, for 14 cases, as a result of authorship determination, one correctly
recognized candidate was obtained, which amounted to 23.3%. In 36 cases, the program was able to
narrow the number of applicants to 3, while in 31 cases the applicant with the greatest structural
similarity was the correctly recognized author (which accounted for 51.7% of the total sample) and in
another 5 cases the correctly recognized author was included in the list of candidates (8.3% of the total
sample). Also, in only 8 cases, the authorship of the text was not determined - none of the submitted
candidates was correctly recognized, which amounted to 13.3%.</p>
      <p>As a result of the obtained data analysis, it can be argued that the size of the confidence interval can
also be considered a specific feature of the author's personal style. So, for some of them, the size of the
confidence interval differs significantly from other authors. It is much larger in A. Vyshnia and M.
Vovchok. It is noteworthy that A. Vyshnia is characterized by his own style of writing, which made it
possible to determine with sufficient accuracy the texts of his authorship, while the style of M. Vovchok
is rather difficult to classify. The minimum interval was obtained for the works of the author V.
Pidmohylnyi, which, however, leads to rather high results of his classification.</p>
      <p>Thus, the percentage of correct authorship identification, taking into account the confidence interval,
was improved to 83.33% (in 50 cases out of 60, the author of the work was correctly recognized).</p>
    </sec>
    <sec id="sec-10">
      <title>5. Discussion</title>
      <p>
        According to our previous studies [
        <xref ref-type="bibr" rid="ref3">3, 23, 24, 25</xref>
        ] on establishing the texts authorship, the initial
result of reliability ranged from 18% of the correct texts attribution to 82% [23] using
character-bycharacter analysis. Later, the result was improved with a range from 80% to 91% using N-grams [24],
genetic algorithm [25] and also working with stems and dictionaries [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>In this paper, the proposed method was used for the first time and results of 75-80% were obtained,
which, taking into account the peculiarities of the Ukrainian language and the complexity of its
formalization for solving the task, correspond to the spread in the percentage of determining the texts
authorship in works devoted to this topic. So, for example, the result of determining authorship is in the
range from 74% to 92% correctly identified cases [26-32]. These results varied depending on the used
method, the language and style of the analyzed text.</p>
      <p>Working with different foreign languages and taking into account their distinctive features, the
authors used various methods.</p>
      <p>In a study of English poets works authorship [30] using the architectures of a convolutional neural
network, a multilayer perceptron, and LSTM neural network, the results ranged from 74-83%. In
another work, using various stylometric functions and algorithms, also in English authors works, the
success rate was 82% [20]. Analyzing text corpora in English and Spanish, working with syllables, the
achieved result was 78.8%. For the Russian language, which is similar in complexity and structure to
Ukrainian, working with a combination of support vector machine and a genetic algorithm, such results
as 82.3% were achieved [27]. And using N-grams in processing the Portuguese language in [31], the
result reached 72%.</p>
      <p>Working with Ukrainian texts, predominantly journalistic style, in view of the structural variability
and complexity of the language, using methods such as neural networks [28] and the Quantitative
Method for Automated Text Authorship Attribution Based on the Statistical Analysis of N-grams
Distribution [29] and working with scientific articles, the authors obtained results of 92% and 79%,
respectively.</p>
      <p>The case of using confidence intervals in determining the authorship of texts has not been found in
recent works, which allows us to assert the novelty of this approach.</p>
      <p>
        Among the works related to text tagging, one can find works devoted to the N-grams [
        <xref ref-type="bibr" rid="ref6">6, 33, 34</xref>
        ].
      </p>
      <p>
        For example, a study [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] of the Coptic language, which is the last phase of the Egyptian language
family and a descendant of the ancient Egyptian script, was conducted to assess the success of tagging
the study of genre, style and authorship in the Coptic language. The results of the study show a relatively
high accuracy of 94-95% correct automatic tagging for literary texts.
      </p>
      <p>In [33] the authors focused on the attribution of the Polish texts authorship using stylometric features
based on part-of-speech tags. The Polish language is characterized by a high level of inflection, so the
authors managed to distinguish more than 1000 tags, which made it possible to build a fairly large
feature space by processing texts and performing their classification using machine learning methods.
The use of this method in highly inflected languages, including Polish, is considered by the authors to
be a promising direction in authorship attribution.</p>
      <p>In [34] for the authorship attribution problem, the use of part-of-speech skip-grams and an in-house
top-k sequential pattern mining algorithm is considered. The authors of the study come to an accuracy
of 86-97% for various authors in training sample.</p>
      <p>Given the differences in the analyzed languages in the presented studies, we can conclude that the
method proposed here is a promising direction for working with Ukrainian literary texts and will
significantly improve the results obtained.</p>
    </sec>
    <sec id="sec-11">
      <title>6. Conclusions</title>
      <p>The paper proposes a new method of text attribution using stochastic formal grammars. Since all
known methods do not give high accuracy and do not take into account the sentence constructing rules,
there is a need to search for new additional methods and new attributes. The characteristic of the
author’s style in the aspect of the sentence constructing is a previously unexplored sphere. Its use, in
combination with already known methods, can increase the efficiency of determining the natural
language texts authorship.</p>
      <p>Analyzing texts with a sample 20x3, the number of matches for the author was 24 out of 30 works.
And working with doubled samples, the result is also positive, but to a lesser extent - 45 out of 60
matches. The results obtained were 80% and 75%, respectively.</p>
      <p>Taking into account the confidence interval, the results were improved to 83.3%. As a result of the
analysis, it can be argued that the size of the confidence interval can also be considered a characteristic
feature of the author's personal style. Thus, a large confidence interval may indicate a low level of
differentiation of the author's style and, as a result, a poor result in determining the authorship of his
works. And vice versa - with a small confidence interval, the probability of confident the author's style
differentiation increases significantly.</p>
      <p>The average value of the works similarity in the training sample is also significant - the higher the
value, the more clearly the style of the author is determined and, accordingly, the result of determining
his works authorship is higher.</p>
      <p>In the future, it is planned to improve the presented method to obtain a better result, and for the same
purpose, it can be combined with previously studied methods. The possibility of more detailed tagging
of sentences parts is considered - working not only parts of speech, but also forms, numbers, gender,
etc. for the word under study. This approach will provide more information about the structure of
sentences and the rules for their construction, specific to a particular author.</p>
    </sec>
    <sec id="sec-12">
      <title>7. References</title>
      <p>[17] G. O. Sidorov, Automatic Authorship Attribution Using Syllables as Classification Features,</p>
      <p>Rhema journal 1 (2018) 62-81.
[18] E. Stamatatos, A survey of modern authorship attribution methods, J. Am. Soc. Inf. Sci. Technol
60 (3) (2009) 538–556.
[19] M. Koppel, J. Schler, S. Argamon, Computational methods in authorship attribution, J. Am. Soc.</p>
      <p>Inf. Sci. Technol 60 (1) (2009) 9–26. doi:10.1002/asi.20961.
[20] M. Koppel, J. Schler, S. Argamon, Authorship attribution: what’s easy and what’s hard?, Lecture</p>
      <p>Notes in Computer Science 7499 (2012) 282-289. doi:10.1007/978-3-642-32790-2_34.
[21] K. Luyckx, W. Daelemans, The effect of author set size and data size in authorship attribution, Lit.</p>
      <p>Linguist. Comput. 26 (1) (2011) 35–55.
[22] P. Mishra, U. Singh, C. M. Pandey, P. Mishra, G. Pandey, Application of student's t-test, analysis
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[23] V. I. Shynkarenko, I. M. Demidovich, Determination of the attributes of authorship of natural texts,</p>
      <p>Artificial Intelligence 3 (2018) 27-35.
[24] V. I. Shynkarenko, I. M. Demidovich Authorship Determination of Natural Language Texts by
Several Classes of Indicators with Customizable Weights, in: Proceedings of the 5th International
Conference on Computational Linguistics and Intelligent Systems (COLINS 2021), Volume I:
Main Conference, Lviv, Ukraine, April 22-23, 2021, pp. 832-844.
[25] I. Demidovich, V. Shynkarenko, O. Kuropiatnyk, O. Kirichenko, Processing Words Effectiveness
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[26] R. Iyer, C. Rosé, A Machine Learning Framework for Authorship Identification FromTexts. ArXiv
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[27] J. Rygl, A. Horák, Authorship Attribution: Comparison of Single-Layer and Double-Layer
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[28] M. Lupei, A. Mitsa, V. Repariuk, V. Sharkan, Identification of authorship of Ukrainian-language
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[29] V. Lytvyn et al., Development of the Quantitative Method for Automated Text Content Authorship
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[30] V. Moshkina, I. Andreeva, N. Yarushkinaa, Solving the problem of determining the author of text
data using a combined assessment, CEUR Workshop 2782 (2020) 112-118.
[31] I. Markov, J. Baptista, O. Pichardo-Lagunas, Authorship Attribution in Portuguese Using
Character N-grams, Acta Polytechnica Hungarica 14(3) (2017) 59–78.
doi:10.12700/APH.14.3.2017.3.4.
[32] G. O. Sidorov, Automatic Authorship Attribution Using Syllables as Classification Features,</p>
      <p>Rhema journal 1 (2018) 62-81.
[33] P. Szwed Authorship Attribution for Polish Texts Based on Part of Speech Tagging. In: Kozielski
S., Mrozek D., Kasprowski P., Małysiak-Mrozek B., Kostrzewa D. (eds) Beyond Databases,
Architectures and Structures. Towards Efficient Solutions for Data Analysis and Knowledge
Representation. BDAS 2017. Communications in Computer and Information Science, vol 716.</p>
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[34] J. Pokou, F. Fournier-Viger, Ch. Moghrabi, Using Frequent Fixed or Variable-Length POS
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    </sec>
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