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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
String concatenation is an associative, but non-commutative operation. The empty string ε serves as the identity element; for any string s, εs = sε = s. Therefore, the set Σ * and the concatenation operation form a monoid, the free monoid generated by Σ.
contains(string,substring) returns boolean Description Returns whether string contains substring as a substring. This is equivalent to using Find and then detecting that it does not result in the failure condition listed in the third column of the Find section. However, some languages have a simpler way of expressing this test. Related
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)".
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 ...
Various operations, such as copying, concatenation, tokenization and searching are supported. For character strings, the standard library uses the convention that strings are null-terminated: a string of n characters is represented as an array of n + 1 elements, the last of which is a "NUL character" with numeric value 0.
Tries support various operations: insertion, deletion, and lookup of a string key. Tries are composed of nodes that contain links, which either point to other suffix child nodes or null . As for every tree, each node but the root is pointed to by only one other node, called its parent .
Suffix trees allow particularly fast implementations of many important string operations. The construction of such a tree for the string S {\displaystyle S} takes time and space linear in the length of S {\displaystyle S} .