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A regular expression (shortened as regex or regexp), [1] sometimes referred to as rational expression, [2] [3] is a sequence of characters that specifies a match pattern in text. Usually such patterns are used by string-searching algorithms for "find" or "find and replace" operations on strings, or for input validation.
The algorithm works recursively by splitting an expression into its constituent subexpressions, from which the NFA will be constructed using a set of rules. [3] More precisely, from a regular expression E, the obtained automaton A with the transition function Δ [clarification needed] respects the following properties:
We consider two such regular expressions equal if they describe the same language. Then A forms a Kleene algebra. In fact, this is a free Kleene algebra in the sense that any equation among regular expressions follows from the Kleene algebra axioms and is therefore valid in every Kleene algebra. Again let Σ be an alphabet.
It is widely used for regular expressions, which is the context in which it was introduced by Stephen Kleene to characterize certain automata, where it means "zero or more repetitions".
In theoretical computer science and formal language theory, a regular language (also called a rational language) [1] [2] is a formal language that can be defined by a regular expression, in the strict sense in theoretical computer science (as opposed to many modern regular expression engines, which are augmented with features that allow the recognition of non-regular languages).
Therefore, the length of the regular expression representing the language accepted by M is at most 1 / 3 (4 n+1 (6s+7)f - f - 3) symbols, where f denotes the number of final states. This exponential blowup is inevitable, because there exist families of DFAs for which any equivalent regular expression must be of exponential size.
MediaWiki's regular expression syntax works like this: Most characters represent themselves. For example, insource:/C-3p0/ will search for pages containing the literal string "C-3p0" (case-sensitive). The following metacharacters are treated specially: . + * ? | { [ ] ( ) " \ # @ < ~. Any metacharacter can be escaped by preceding it with a ...
A regular expression may be used to conveniently describe an advanced search pattern in a "find and replace"–like operation of a text processing utility. Glushkov's algorithm can be used to transform it into an NFA, which furthermore is small by nature, as the number of its states equals the number of symbols of the regular expression, plus one.