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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} .
String functions are used in computer programming languages to manipulate a string or query information about a string (some do both).. Most programming languages that have a string datatype will have some string functions although there may be other low-level ways within each language to handle strings directly.
A primary purpose of strings is to store human-readable text, like words and sentences. Strings are used to communicate information from a computer program to the user of the program. [2] A program may also accept string input from its user. Further, strings may store data expressed as characters yet not intended for human reading.
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 length of a string is the number of code units before the zero code unit. [1] The memory occupied by a string is always one more code unit than the length, as space is needed to store the zero terminator. Generally, the term string means a string where the code unit is of type char, which is exactly 8 bits on all modern machines.
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.