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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.
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).
For example, the alphabet of lowercase letters "a" through "z" can be used to form English words like "iceberg" while the alphabet of both upper and lower case letters can also be used to form proper names like "Wikipedia". A common alphabet is {0,1}, the binary alphabet, and a "00101111" is an example of a binary string.
The expression regex denotes a regular expression in MediaWiki-flavored regular expression syntax. ... [a-z]{2}/ matches exactly 2 lowercase letters in a row ...
Given a set of strings (also called "positive examples"), the task of regular language induction is to come up with a regular expression that denotes a set containing all of them. As an example, given {1, 10, 100}, a "natural" description could be the regular expression 1⋅0 * , corresponding to the informal characterization " a 1 followed by ...
A word over an alphabet can be any finite sequence (i.e., string) of letters. The set of all words over an alphabet Σ is usually denoted by Σ * (using the Kleene star). The length of a word is the number of letters it is composed of. For any alphabet, there is only one word of length 0, the empty word, which is often denoted by e, ε, λ or ...
The remaining, more difficult part, is to prove that for there is no equivalent regular expression of star height less than n; a proof is given in Eggan (1963). However, Eggan's examples use a large alphabet , of size 2 n -1 for the language with star height n .
Given a finite alphabet A of symbols, [6] a generalized regular expression R denotes a possibly infinite set of finite-length strings over the alphabet A, called the language of R, denoted L(R). A generalized regular expression can be one of the following (where a is a symbol of the alphabet A , and R and S are generalized regular expressions):