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The Wagner–Fischer algorithm computes edit distance based on the observation that if we reserve a matrix to hold the edit distances between all prefixes of the first string and all prefixes of the second, then we can compute the values in the matrix by flood filling the matrix, and thus find the distance between the two full strings as the last value computed.
Many authors also use concatenation of a string set and a single string, and vice versa, which are defined similarly by S 1 w = { vw : v ∈ S 1} and vS 2 = { vw : w ∈ S 2}. In these definitions, the string vw is the ordinary concatenation of strings v and w as defined in the introductory section.
Generalized suffix tree for the strings "ABAB", "BABA" and "ABBA", numbered 0, 1 and 2. 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 ...
For function that manipulate strings, modern object-oriented languages, like C# and Java have immutable strings and return a copy (in newly allocated dynamic memory), while others, like C manipulate the original string unless the programmer copies data to a new string.
A string homomorphism (often referred to simply as a homomorphism in formal language theory) is a string substitution such that each character is replaced by a single string. That is, f ( a ) = s {\displaystyle f(a)=s} , where s {\displaystyle s} is a string, for each character a {\displaystyle a} .
Concatenation theory, also called string theory, character-string theory, or theoretical syntax, studies character strings over finite alphabets of characters, signs, symbols, or marks. String theory is foundational for formal linguistics , computer science, logic, and metamathematics especially proof theory. [ 1 ]
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In computer programming, array slicing is an operation that extracts a subset of elements from an array and packages them as another array, possibly in a different dimension from the original.