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Regular Expression


Regular expressions define formal languages as sets of strings over a finite alphabet. Let sigma denote a selected alphabet. Then emptyset is a regular expression that denotes the empty set and epsilon is a regular expression that denotes the set containing the empty string as its only element.

If c in sigma, then c is a regular expression that denotes the set whose only element is string c. If p and q are regular expressions denoting sets L(p) and L(q), then

1. (p)|(q) is a regular expression denoting the set L(p) union L(q), where  union denotes the union.

2. (p)(q) is a regular expression denoting the set of all concatenations of m and n, where m in L(p) and n in L(q).

3. (p)^* is a regular expression denoting closure of L(p), that is, the set of zero or more concatenations of strings from L(p)

The sets defined by regular expressions are called regular sets, and a set is regular iff it is defined by a right linear grammar.


See also

Formal Language, Grammar

This entry contributed by Alex Sakharov (author's link)

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References

Aho, A. V. and Ullman J. D. Theory of Parsing, Translation and Compiling, Vol. 1. Englewood Cliffs, NJ: Prentice Hall, 1972.Aho, A. V. and Ullman J. D. Theory of Parsing, Translation and Compiling, Vol. 2. Englewood Cliffs, NJ: Prentice Hall, 1972.

Referenced on Wolfram|Alpha

Regular Expression

Cite this as:

Sakharov, Alex. "Regular Expression." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/RegularExpression.html

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