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| | Hi there. My name is Sophia Meagher even though it is not the title on my birth certificate. My spouse and I live in Kentucky. My spouse doesn't like it the way I do but what I really like performing is caving but I don't have the time recently. Office supervising is what she does for a living.<br><br>Also visit my page :: good psychic ([http://cartoonkorea.com/ce002/1093612 Read A lot more]) |
| In [[formal language]]s, which are used in [[mathematical logic]] and [[theoretical computer science]], '''stringology''' deals with algorithms and data structures used for [[String (computer science)|string]] processing. The name was coined in 1984 by computer scientist [[Zvi Galil]].<ref>http://www.stringology.org/</ref>
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| ==Formal theory==
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| <!-- This section is linked from Sequence -->
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| {{See also|Tuple}}
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| Let Σ be an ''alphabet'', a [[empty set|non-empty]] [[finite set|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.
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| 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''.
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| The set of all strings over Σ of length ''n'' is denoted Σ<sup>''n''</sup>. For example, if Σ = {0, 1}, then Σ<sup>2</sup> = {00, 01, 10, 11}. Note that Σ<sup>0</sup> = {ε} for any alphabet Σ.
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| The set of all strings over Σ of any length is the [[Kleene star|Kleene closure]] of Σ and is denoted Σ*. In terms of Σ<sup>''n''</sup>,
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| :<math>\Sigma^{*} = \bigcup_{n \in \N} \Sigma^{n}</math> | |
| 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.
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| 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 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.
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| ===Topology===
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| Strings admit the following interpretation as nodes on a graph:
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| * Fixed-length strings can be viewed as nodes on a [[hypercube]]
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| * Variable-length strings (of finite length) can be viewed as nodes on the [[k-ary tree|''k''-ary tree]], where ''k'' is the number of symbols in Σ
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| * Infinite strings can be viewed as infinite paths on the ''k''-ary tree.
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| The natural topology on the set of fixed-length strings or variable length strings is the discrete topology, but the natural topology on the set of infinite strings is the [[limit topology]], viewing the set of infinite strings as the [[inverse limit]] of the sets of finite strings. This is the construction used for the [[p-adic|''p''-adic numbers]] and some constructions of the [[Cantor set]], and yields the same topology.
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| ==String processing algorithms==
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| There are many [[algorithm]]s for processing strings, each with various trade-offs. Some categories of algorithms include:
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| * [[String searching algorithm]]s for finding a given substring or pattern
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| * [[String manipulation algorithm]]s
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| * [[Sorting algorithm]]s
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| * [[Regular expression]] algorithms
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| * [[Parser|Parsing]] a string
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| * [[Sequence mining]]
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| Advanced string algorithms often employ complex mechanisms and data structures, among them [[suffix tree]]s and [[finite state machine]]s.
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| ==Character string functions==
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| {{See also|Comparison of programming languages (string functions)}}
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| [[String Functions (Computer Science)|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 [[programming language|computer programming language]].
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| The most basic example of a string function is the <code>length(string)</code> function, which returns the length of a string (not counting any terminator characters or any of the string's internal structural information) and does not modify the string. For example, <code>length("hello</code> <code>world")</code> returns 11.
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| There are many string functions that 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 <code>len(string)</code>. 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 results.
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| ==See also==
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| {{col-begin}}
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| {{col-break|width=33%}}
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| * [[string (computer science)]]
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| * [[Rope (computer science)|Rope]]
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| * [[Bitstring]]
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| * [[Improper input validation]]
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| * [[Incompressible string]]
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| * [[Empty string]]
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| {{col-break}}
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| * Formal language
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| * [[String metric]]
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| * [[:Category:Algorithms on strings]]
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| {{col-end}}
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| ==References==
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| {{reflist|2}}
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| {{Data types}}
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| {{DEFAULTSORT:String (Computer Science)}}
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| [[Category:Algorithms on strings| ]]
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| [[Category:String (computer science)| ]]
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| [[Category:Character encoding]]
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| [[Category:Data types]]
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| [[Category:Formal languages]]
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| [[Category:Combinatorics on words]]
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| [[Category:Primitive types]]
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| [[Category:Syntactic entities]]
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