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In formal language theory and pattern matching (including regular expressions), the concatenation operation on strings is generalised to an operation on sets of strings as follows: For two sets of strings S 1 and S 2, the concatenation S 1 S 2 consists of all strings of the form vw where v is a string from S 1 and w is a string from S 2, or ...
Like raw strings, there can be any number of equals signs between the square brackets, provided both the opening and closing tags have a matching number of equals signs; this allows nesting as long as nested block comments/raw strings use a different number of equals signs than their enclosing comment: --[[comment --[=[ nested comment ...
COBOL uses the STRING statement to concatenate string variables. MATLAB and Octave use the syntax "[x y]" to concatenate x and y. Visual Basic and Visual Basic .NET can also use the "+" sign but at the risk of ambiguity if a string representing a number and a number are together. Microsoft Excel allows both "&" and the function "=CONCATENATE(X,Y)".
Some other tailor-made equality, preserving the external behavior. For example, 1/2 and 2/4 are considered equal when seen as a rational number. A possible requirement would be that "A = B if and only if all operations on objects A and B will have the same result", in addition to reflexivity, symmetry, and transitivity.
In information theory, the Hamming distance between two strings or vectors of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other, or equivalently, the minimum number of errors that could have transformed one string into the other.
In the array containing the E(x, y) values, we then choose the minimal value in the last row, let it be E(x 2, y 2), and follow the path of computation backwards, back to the row number 0. If the field we arrived at was E(0, y 1), then T[y 1 + 1] ... T[y 2] is a substring of T with the minimal edit distance to the pattern P.
Various algorithms exist that solve problems beside the computation of distance between a pair of strings, to solve related types of problems. Hirschberg's algorithm computes the optimal alignment of two strings, where optimality is defined as minimizing edit distance. Approximate string matching can be formulated in terms of edit distance.
The second case reduces to the first by splitting the string at the split point to create two new leaf nodes, then creating a new node that is the parent of the two component strings. For example, to split the 22-character rope pictured in Figure 2.3 into two equal component ropes of length 11, query the 12th character to locate the node K at ...