## 3 Materials and Methods
\begin{array}{l}K_{1}=\big{\{}n_{1},n_{2},\ldots,n_{g}\big{\}},\\ K_{2}=\big{\{}n_{2},n_{3},\ldots,n_{g+1}\big{\}},\\ \ldots\\ K_{v-g+1}=\big{\{}n_{v-g+1},n_{v-g+2},\ldots,n_{v-1},n_{v}\big{\}},\end{array}  \tag{9}\]  
where \(v\) is the number of elements in a sequence \(N\), and \(g\) is the window size or number of elements in subsequences \(K_{1},K_{2},\ldots,K_{v-g+1}\). Since the elements of the constructed subsequences are real numbers, \(n_{i}\in R,i=\overline{1,v}\), then these subsequences can be considered as \(g\)-dimensional vectors. If we assume that the space is given \(R^{g}\) with a Euclidean structure, then we can define a metric on this space \(p\) between any two vectors of space \(a\in R^{g}\) and \(b\in R^{g}\): \(\rho(a,b)\). In this case, this metric will satisfy the axioms of identity, that is, \(\rho(a,b)=0\Leftrightarrow a=b\), axiom of symmetry: \(\rho(a,b)=\rho(b,a)\) and the triangle axiom for some vector \(c\in R^{g}\): \(\rho(a,c)\leq\rho(a,b)+\rho(b,c)\). Such a distance or similarity measure between the vectors representing the numerical values of the content of the tables is a component that determines the degree of similarity of these tables. In accordance with the statement of the problem, let B be the input table, and \(B_{1},B_{2},\ldots,B_{p}\) be the tables that are selected and stored in a common table base, where \(p\) is the number of tables in the base. The task is to identify those tables from the base for which the condition \(F\big{(}B,\widetilde{B}_{i}\big{)}<\lambda,i=\overline{1,1}\) is satisfied. Let a sequence of text data be constructed, \(S=\{s_{1},s_{2},\ldots,s_{w}\}\), and a sequence of numerical values \(N=\{n_{1},n_{2},\ldots,n_{v}\}\) for the table B. Since the base of the tables is already known, it is obvious that each such table is indexed. Thus, for each of the tables \(B_{1},B_{2},\ldots,B_{p}\) there are known sequences of text data \(S^{y}=\big{\{}s_{1}^{y},s_{2}^{y},\ldots,s_{w}^{y}\big{\}}\) and sequences of numerical data \(N^{y}=\big{\{}n_{1}^{y},n_{2}^{y},\ldots,n_{v}^{y}\big{\}}\), \(y=\overline{1,p}\). It is also obvious that index elements are given for word sequences:  
\[I\big{(}E_{k_{y}}^{y}\big{)}=\Big{\{}g_{k_{y}1}^{y},\delta_{k_{y}2}^{y},\ldots,\delta_{k_{y}c}^{y}\Big{\}}, \tag{10}\]  
where \(\delta_{k_{y}x}^{y}\in\{0,1\}\), \(k_{y}=\overline{1,m_{y}-h+1}\), \(x=\overline{1,c}\), \(c\) is the number of bits in a bit sequence, and \(m_{y}\) is the number of words in the sequences:  
\[W^{y}=\Big{\{}S_{1}^{y,\beta_{1}},S_{2}^{y,\beta_{2}},\ldots,S_{m_{y}}^{y, \beta_{m_{y}}}\Big{\}} \tag{11}\]  
containing words \(S_{y}^{y,\beta_{y}}\) in canonical form, where \(\beta_{y},j=\overline{1,m_{y}}\) is word lengths. We construct a string sequence \(S=\{s_{1},s_{2},\ldots,s_{w}\}\) input table B unigram of words in canonized form:  
\[W=\Big{\{}S_{1}^{\beta_{1}},S_{2}^{\beta_{2}},\ldots,S_{m}^{\beta_{m}}\Big{\}}, \tag{12}\]  
where \(\beta_{y},j=\overline{1,m}\) is word lengths, and \(m\) is their number. Next, using the sliding window method, we determine the sequences \(E_{1},E_{2},\ldots,E_{m-h+1}\) and, using the locality-sensitive hashing method, we construct the index elements:  
\[I(E_{k})=\{s_{k1},\delta_{k2},\ldots,\delta_{kc}\}, \tag{13}\]  
where \(\delta_{kx}\in\{0,1\}\), \(k=\overline{1,m-h+1}\), \(x=\overline{1,c}\), and \(c\) is the number of bits representing the sequence. We calculate the Hamming distances between the elements of each index of the input table sequences and the elements of the indexes of the table sequences in the database using the formula:  
\[H\Big{(}I(E_{k}),I\Big{(}E_{k_{y}}^{y}\Big{)}\Big{)}=\frac{1}{c}\sum_{j=1}^{c }\Bigl{|}\delta_{kj}-\delta_{k_{yj}}\Bigr{|}, \tag{14}\]  
where \(k=\overline{1,m-h+1}\), \(k_{y}=\overline{1,m_{y}-h+1}\), \(y=\overline{1,p}\).