String (computer science)
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In computer programming and formal language theory, (and other branches of mathematics), a string is an ordered sequence of symbols. These symbols are chosen from a predetermined set.
In programming, when stored in memory each symbol is represented using a numeric value. A variable declared to have a string datatype usually causes storage to be allocated in memory that is capable of holding some predetermined number of symbols. When it appears in source code a string is known as a string literal and has a representation that denotes it as such. Sometimes the term binary string is used to refer to an arbitrary sequence of bits.
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[edit] Formal theory
Let Σ be an alphabet, a non-empty finite set. Elements of Σ are called symbols or characters. A string (or word) over Σ is any finite sequence of characters from Σ. For example, if Σ = {0, 1}, then 0101 is a string over Σ.
The length of a string is the number of characters in the string (the length of the sequence) and can be any non-negative integer. The empty string is the unique string over Σ of length 0, and is denoted ε or λ.
The set of all strings over Σ of length n is denoted Σn. For example, if Σ = {0, 1}, then Σ2 = {00, 01, 10, 11}. Note that Σ0 = {ε} for any alphabet Σ.
The set of all strings over Σ of any length is the Kleene closure of Σ and is denoted Σ*. In terms of Σn, 
. For example, if Σ = {0, 1}, Σ* = {ε, 0, 1, 00, 01, 10, 11, 000, 001, 010, 011, …}. Although Σ* itself is countably infinite, all elements of Σ* have finite length.
A set of strings over Σ (i.e. any subset of Σ*) is called a formal language over Σ. For example, if Σ = {0, 1}, the of the set of strings with an even number of zeros ({ε, 1, 00, 11, 001, 010, 100, 111, 0000, 0011, 0101, 0110, 1001, 1010, 1100, 1111, …}) is a formal language over Σ*.
[edit] Concatenation and substrings
Concatenation is an important binary operation on Σ*. For any two strings s and t in Σ*, their concatenation is defined as the sequence of characters in s followed by the sequence of characters in t, and is denoted st. For example, if Σ = {a, b, …, z}, s = bear, and t = hug, then st = bearhug and ts = hugbear.
String concatenation is an associative, but non-commutative operation. The empty string 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. In addition, the length function defines a monoid homomorphism from Σ* to the non-negative integers.
A string s is said to be a substring or factor of t if there exist (possibly empty) strings u and v such that t = usv. The relation "is a substring of" defines a partial order on Σ*, the least element of which is the empty string.
[edit] Lexicographical ordering
It is often necessary to define an ordering on the set of strings. If the alphabet Σ has a total order (cf. alphabetical order) one can define a total order on Σ* called lexicographical order. Note that since Σ is finite, it is always possible to define a well ordering on Σ and thus on Σ*. For example, of Σ = {0, 1} and 0 < 1, then the lexicographical ordering of Σ* is ε < 0 < 00 < 000 < … < 011 < 0110 < … < 01111 < … < 1 < 10 < 100 < … < 101 < … < 111 …
[edit] String datatypes
A string datatype is a datatype modeled on the idea of a formal string. Strings are such an important and useful datatype that they are implemented in nearly every programming language. In some languages they are available as primitive types and in others as composite types. The syntax of most high-level programming languages allows for a string, usually quoted in some way, to represent an instance of a string datatype; such a meta-string is called a literal or string literal.
[edit] String length
Although formal strings can have an arbitrary (but finite) length, the length of strings in real languages is often constrained to an artificial maximum. In general, there are two types of string datatypes: fixed length strings which have a fixed maximum length and which use the same amount of memory whether this maximum is reached or not, and variable length strings whose length is not arbitrarily fixed and which use varying amounts of memory depending on their actual size. Most strings in modern programming languages are variable length strings. Despite the name, even variable length strings are limited in length; although, generally, the limit depends only on the amount of memory available.
[edit] Character encoding
Historically, string datatypes had one byte for each character, and although the exact character set varied by region, the character encodings were similar enough that programmers could generally get away with ignoring this — groups of character sets used by the same system in different regions either had a character in the same place, or did not have it at all. Mostly these character sets were based on ASCII, though IBM's mainframe systems went their own way and used EBCDIC.
Logographic languages such as Chinese, Japanese and Korean (known collectively as CJK) need far more than 256 characters — the limit of a one-byte-per-character encoding — for reasonable representation. The normal solutions involved keeping single-byte representations for ASCII and using two-byte representations for CJK ideographs. Use of these with existing code led to problems with matching and cutting of strings, the severity of which depended on how the character encoding was designed. Some encodings such as the EUC family guarantee that a byte value in the ASCII range will only represent that ASCII character making the encoding safe for systems that use those characters as field separators or similar. Others such as ISO-2022 and shift-jis do not make such guarantees, making matching on byte codes unsafe. Another issue is that if the beginning of a string is cut off, important instructions for the decoder or information on position in a multibyte sequence may be lost. Another issue is that if strings are joined together (especially after having their ends truncated by code not aware of the encoding), the first string may not leave the encoder in a state suitable for dealing with the second string.
Unicode has complicated the picture somewhat. Most languages have a datatype for Unicode strings (usually UTF-16 as it was usually added before Unicode supplemental planes were introduced). Converting between Unicode and local encodings requires an understanding of the local encoding, which may be problematic for existing systems where strings of various encodings are being transmitted together with no real marking as to what encoding they are in.
[edit] Implementations
Some languages like C++ implement strings as templates that can be used with any primitive type, but this is the exception, not the rule.
If an object-oriented language represents strings as objects, they are called mutable if the value can change at runtime and immutable if the value is frozen after creation. For example, Ruby has mutable strings, while Python's strings are immutable.
[edit] Representations
Representations of strings depend heavily on the choice of character repertoire and the method of character encoding. Older string implementations were designed to work with repertoire and encoding defined by ASCII, or more recent extensions like the ISO 8859 series. Modern implementations often use the extensive repertoire defined by Unicode along with a variety of complex encodings such as UTF-8 and UTF-16.
Most string implementations are very similar to variable-length arrays with the entries storing the character codes of corresponding characters. The principal difference is that, with certain encodings, a single logical character may take up more than one entry in the array. This happens for example with UTF-8, where single characters can take anywhere from one to four bytes. In these cases, the logical length of the string differs from the logical length of the array.
The length of a string can be stored implicitly by using a special terminating character; often this is the null character having value zero, a convention used and perpetuated by the popular C programming language. Hence, this representation is commonly referred to as C string. The length of a string can also be stored explicitly, for example by prefixing the string with byte value — a convention used in Pascal; consequently some people call it a P-string.
In terminated strings, the terminating code is not an allowable character in any string.
Here is an example of a null-terminated string stored in a 10-byte buffer, along with its ASCII representation:
| F | R | A | N | K | NUL | k | e | f | w |
| 46 | 52 | 41 | 4E | 4B | 00 | 6B | 65 | 66 | 77 |
The length of a string in the above example 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 another string or just garbage. (Strings of this form are sometimes called ASCIZ strings, after the original assembly language directive used to declare them.)
Here is the equivalent (old style) Pascal string stored in a 10-byte buffer, along with its ASCII representation:
| length | F | R | A | N | K | k | f | f | w |
| 05 | 46 | 52 | 41 | 4E | 4B | 6B | 66 | 66 | 77 |
While these representations are common, others are possible. Using ropes makes certain string operations, such as insertions, deletions, and concatenations more efficient.
[edit] Vectors
While character strings are very common uses of strings, a string in computer science may refer generically to any vector of homogenously typed data. A string of bits or bytes, for example, may be used to represent data retrieved from a communications medium. This data may or may not be represented by a string-specific datatype, depending on the needs of the application, the desire of the programmer, and the capabilities of the programming language being used.
[edit] String processing algorithms
There are many algorithms for processing strings, each with various trade-offs. Some categories of algorithms include
- string searching algorithms for finding a given substring or pattern;
- string manipulation algorithms;
- sorting algorithms;
- regular expression algorithms; and
- parsing a string.
Advanced string algorithms often employ complex mechanisms and data structures, among them suffix trees and finite state machines.
[edit] Character string oriented languages and utilities
Character strings are such a useful datatype that several languages have been designed in order to make string processing applications easy to write. Examples include the following languages:
Many UNIX utilities perform simple string manipulations and can be used to easily program some powerful string processing algorithms. Files and finite streams may be viewed as strings.
Several string libraries for the C and C++ programming languages do exist which add greater functionality for string processing in those languages:
- The Better String Library
- The Vstr String Library
- Perl Compatible Regular Expressions
- Comparison page for C/C++ string libraries
Some APIs like Multimedia Control Interface, embedded SQL or printf use strings to hold commands that will be interpreted.
Recent scripting programming languages, including Perl, Python, Ruby, and Tcl employ regular expressions to facilitate text operations.
[edit] Character string functions
String functions are used to manipulate a string or change or edit the contents of a string. They also are used to query information about a string. They are usually used within the context of a computer programming language.
The most basic example of a string function is the length(string) function. This function returns the length of a string (not counting the null terminator or any other of the string's internal structural information) and does not change the string.
eg. length("hello world") would return 11.
There are many string functions which exist in other languages with similar or exactly the same syntax or parameters. For example in many languages the length function is usually represented as len(string). Even though string functions are very useful to a computer programmer, a computer programmer using these functions should be mindful that a string function in one language could in another language behave differently or have a similar or completely different function name, parameters, syntax and outcomes.
