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A string is a substring (or factor) [1] of a string if there exists two strings and such that =.In particular, the empty string is a substring of every string. Example: The string = ana is equal to substrings (and subsequences) of = banana at two different offsets:
A PrintableString is a restricted character string type in the ASN.1 notation. It is used to describe data that consists only of a specific printable subset of the ASCII character set. According to the ASN.1 Specification of basic notation, [ 1 ] the character set of PrintableString can be expressed as:
The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string ...
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.
The most widely known string metric is a rudimentary one called the Levenshtein distance (also known as edit distance). [2] It operates between two input strings, returning a number equivalent to the number of substitutions and deletions needed in order to transform one input string into another.
The similarity of two strings and is determined by this formula: twice the number of matching characters divided by the total number of characters of both strings. The matching characters are defined as some longest common substring [3] plus recursively the number of matching characters in the non-matching regions on both sides of the longest common substring: [2] [4]
More formally, for any language L and string x over an alphabet Σ, the language edit distance d(L, x) is given by [14] (,) = (,), where (,) is the string edit distance. When the language L is context free , there is a cubic time dynamic programming algorithm proposed by Aho and Peterson in 1972 which computes the language edit distance. [ 15 ]
Computing E(m, j) is very similar to computing the edit distance between two strings. In fact, we can use the Levenshtein distance computing algorithm for E ( m , j ), the only difference being that we must initialize the first row with zeros, and save the path of computation, that is, whether we used E ( i − 1, j ), E( i , j − 1) or E ( i ...