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String homomorphisms are monoid morphisms on the free monoid, preserving the empty string and the binary operation of string concatenation. Given a language , the set () is called the homomorphic image of . The inverse homomorphic image of a string is defined as
Definition: Split (i, S): split the string S into two new strings S 1 and S 2, S 1 = C 1, ..., C i and S 2 = C i + 1, ..., C m. Time complexity: () There are two cases that must be dealt with: The split point is at the end of a string (i.e. after the last character of a leaf node) The split point is in the middle of a string.
The strings over an alphabet, with the concatenation operation, form an associative algebraic structure with identity element the null string—a free monoid. Sets of strings with concatenation and alternation form a semiring , with concatenation (*) distributing over alternation (+); 0 is the empty set and 1 the set consisting of just the null ...
The length of the string in the above example, "FRANK", is 5 characters, but it occupies 6 bytes. Characters after the terminator do not form part of the representation; they may be either part of other data or just garbage. (Strings of this form are sometimes called ASCIZ strings, after the original assembly language directive used to declare ...
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 ...
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)".
String search, in O(m) complexity, where m is the length of the sub-string (but with initial O(n) time required to build the suffix tree for the string) Finding the longest repeated substring Finding the longest common substring
A string is a prefix [1] of a string if there exists a string such that =. A proper prefix of a string is not equal to the string itself; [2] some sources [3] in addition restrict a proper prefix to be non-empty. A prefix can be seen as a special case of a substring.