Regular expression - Wikipedia

Regular expression - Wikipedia
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Sequence of characters that forms a search pattern
"Regex" redirects here. For the comic book, see
Re:Gex
".*" redirects here. For the C++ operator, see
Pointer (computer science) § Pointer-to-member
Blue
highlights show the match results of the regular expression pattern:
/r[aeiou]+/
(lowercase
followed by one or more lowercase vowels).
regular expression
(shortened as
regex
or
regexp
),
sometimes referred to as a
rational expression
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
. Regular expression techniques are developed in
theoretical computer science
and
formal language
theory.
The concept of regular expressions began in the 1950s, when the American mathematician
Stephen Cole Kleene
formalized the concept of a
regular language
. They came into common use with
Unix
text-processing utilities. Different
syntaxes
for writing regular expressions have existed since the 1980s, one being the
POSIX
standard and another, widely used, being the
Perl
syntax.
Regular expressions are used in
search engines
, in search and replace dialogs of
word processors
and
text editors
, in
text processing
utilities such as
sed
and
AWK
, and in
lexical analysis
. Regular expressions are supported in many programming languages. Library implementations are often called an "
engine
",
and
many of these
are available for reuse.
History
edit
Stephen Cole Kleene
, who introduced the concept
Regular expressions originated in 1951, when mathematician
Stephen Cole Kleene
described
regular languages
using his mathematical notation called
regular events
These arose in
theoretical computer science
, in the subfields of
automata theory
(models of computation) and the description and classification of
formal languages
, motivated by Kleene's attempt to describe early
artificial neural networks
. (Kleene introduced it as an alternative to
McCulloch & Pitts's
"prehensible", but admitted "We would welcome any suggestions as to a more descriptive term."
) Other early implementations of
pattern matching
include the
SNOBOL
language, which did not use regular expressions, but instead its own pattern matching constructs.
Regular expressions entered popular use from 1968 in two uses: pattern matching in a text editor
and lexical analysis in a compiler.
10
Among the first appearances of regular expressions in program form was when
Ken Thompson
built Kleene's notation into the editor
QED
as a means to match patterns in
text files
11
12
13
For speed, Thompson implemented regular expression matching by
just-in-time compilation
(JIT) to
IBM 7094
code on the
Compatible Time-Sharing System
, an important early example of JIT compilation.
14
He later added this capability to the Unix editor
ed
, which eventually led to the popular search tool
grep
's use of regular expressions ("grep" is a word derived from the command for regular expression searching in the ed editor:
g/
re
/p
meaning "Global search for Regular Expression and Print matching lines").
15
Around the same time that Thompson developed QED, a group of researchers including
Douglas T. Ross
implemented a tool based on regular expressions that is used for lexical analysis in
compiler
design.
10
Many variations of these original forms of regular expressions were used in
Unix
13
programs at
Bell Labs
in the 1970s, including
lex
sed
AWK
, and
expr
, and in other programs such as
vi
, and
Emacs
(which has its own, incompatible syntax and behavior). Regexes were subsequently adopted by a wide range of programs, with these early forms standardized in the
POSIX.2
standard in 1992.
In the 1980s, the more complicated regexes arose in
Perl
, which originally derived from a regex library written by
Henry Spencer
(1986), who later wrote an implementation for
Tcl
called
Advanced Regular Expressions
16
The Tcl library is a hybrid
NFA
DFA
implementation with improved performance characteristics. Software projects that have adopted Spencer's Tcl regular expression implementation include
PostgreSQL
17
Perl later expanded on Spencer's original library to add many new features.
18
Part of the effort in the design of
Raku
(formerly named Perl 6) is to improve Perl's regex integration, and to increase their scope and capabilities to allow the definition of
parsing expression grammars
19
The result is a
mini-language
called
Raku rules
, which are used to define Raku grammar as well as provide a tool to programmers in the language. These rules maintain existing features of Perl 5.x regexes, but also allow
BNF
-style definition of a
recursive descent parser
via sub-rules.
The use of regexes in structured information standards for document and database modeling started in the 1960s and expanded in the 1980s when industry standards like
ISO SGML
(precursored by ANSI "GCA 101-1983") consolidated. The kernel of the
structure specification language
standards consists of regexes. Its use is evident in the
DTD
element group syntax. Prior to the use of regular expressions, many search languages allowed simple wildcards, for example "*" to match any sequence of characters, and "?" to match a single character. Relics of this can be found today in the
glob
syntax for filenames, and in the
SQL
LIKE
operator.
Starting in 1997,
Philip Hazel
developed
PCRE
(Perl Compatible Regular Expressions), which attempts to closely mimic Perl's regex functionality and is used by many modern tools including
PHP
and
Apache HTTP Server
20
Today, regexes are widely supported in programming languages, text processing programs (particularly
lexers
), advanced text editors, and some other programs. Regex support is part of the
standard library
of many programming languages, including
Java
and
Python
, and is built into the syntax of others, including Perl and
ECMAScript
. In the late 2010s, several companies started to offer hardware,
FPGA
21
GPU
22
implementations of
PCRE
compatible regex engines that are faster compared to
CPU
implementations
Patterns
edit
The phrase
regular expressions
, or
regexes
, is often used to mean the specific, standard textual syntax for representing patterns for matching text, as distinct from the mathematical notation described below. Each character in a regular expression (that is, each character in the string describing its pattern) is either a
metacharacter
, having a special meaning, or a regular character that has a literal meaning. For example, in the regex
b.
, 'b' is a literal character that matches just 'b', while '.' is a metacharacter that matches every character except a newline. Therefore, this regex matches, for example, 'b%', or 'bx', or 'b5'. Together, metacharacters and literal characters can be used to identify text of a given pattern or process a number of instances of it. Pattern matches may vary from a precise equality to a very general similarity, as controlled by the metacharacters. For example,
is a very general pattern,
[a-z]
(match all lowercase letters from 'a' to 'z') is less general and
is a precise pattern (matches just 'b'). The metacharacter syntax is designed specifically to represent prescribed targets in a concise and flexible way to direct the automation of text processing of a variety of input data, in a form easy to type using a standard
ASCII
keyboard
A very simple case of a regular expression in this syntax is to locate a word spelled two different ways in a
text editor
; for example, the regular expression
seriali[sz]e
matches both "serialise" and "serialize".
Wildcard characters
also achieve this, but are more limited in what they can pattern, as they have fewer metacharacters and a simple language-base.
The usual context of wildcard characters is in
globbing
similar names in a list of files, whereas regexes are usually employed in applications that pattern-match text strings in general. For example, the regex
[ \t]
+|
[ \t]
+$
matches excess whitespace at the beginning or end of a line. An advanced regular expression that matches any numeral is
[+-]
?(
+(
*)?|
+)(
[eE][+-]
+)?
Translating
the
Kleene star
* means "zero or more of
")
regex processor
translates a regular expression in the above syntax into an internal representation that can be executed and matched against a
string
representing the text being searched in. One possible approach is the
Thompson's construction algorithm
to construct a
nondeterministic finite automaton
(NFA), which is then
made deterministic
and the resulting
deterministic finite automaton
(DFA) is run on the target text string to recognize substrings that match the regular expression.
The picture shows the NFA scheme
*)
obtained from the regular expression
, where
denotes a simpler regular expression in turn, which has already been
recursively
translated to the NFA
).
Basic concepts
edit
A regular expression, often called a
pattern
, specifies a
set
of strings required for a particular purpose. A simple way to specify a finite set of strings is to list its
elements
or members. However, there are often more concise ways: for example, the set containing the three strings "Handel", "Händel", and "Haendel" can be specified by the pattern
H(ä|ae?)ndel
; we say that this pattern
matches
each of the three strings. However, there can be many ways to write a regular expression for the same set of strings: for example,
(Hän|Han|Haen)del
also specifies the same set of three strings in this example.
Most formalisms provide the following operations to construct regular expressions.
Boolean "or"
vertical bar
separates alternatives. For example,
gray
grey
can match "gray" or "grey".
Grouping
Parentheses
are used to define the scope and precedence of the
operators
(among other uses). For example,
gray|grey
and
gr
are equivalent patterns which both describe the set of "gray" or "grey".
Quantification
quantifier
after an element (such as a
token
, character, or group) specifies how many times the preceding element is allowed to repeat. The most common quantifiers are the
question mark
, the
asterisk
(derived from the
Kleene star
), and the
plus sign
Kleene plus
).
The question mark indicates
zero or one
occurrences of the preceding element. For example,
colou?r
matches both "color" and "colour".
The asterisk indicates
zero or more
occurrences of the preceding element. For example,
ab*c
matches "ac", "abc", "abbc", "abbbc", and so on.
The plus sign indicates
one or more
occurrences of the preceding element. For example,
ab+c
matches "abc", "abbc", "abbbc", and so on, but not "ac".
{n}
23
The preceding item is matched exactly
times.
{min,}
23
The preceding item is matched
min
or more times.
{,max}
23
The preceding item is matched up to
max
times.
{min,max}
23
The preceding item is matched at least
min
times, but not more than
max
times.
Wildcard
The wildcard
matches any character. For example,
a.b
matches any string that contains an "a", and then any character and then "b".
a.*b
matches any string that contains an "a", and then the character "b" at some later point.
These constructions can be combined to form arbitrarily complex expressions, much like one can construct arithmetical expressions from numbers and the operations +, −, ×, and ÷.
The precise
syntax
for regular expressions varies among tools and with context; more detail is given in
§ Syntax
Formal language theory
edit
Regular expressions describe
regular languages
in
formal language theory
. They have the same expressive power as
regular grammars
. But the language of regular expressions itself, is
context-free language
Formal definition
edit
Regular expressions consist of constants, which denote sets of strings, and operator symbols, which denote operations over these sets. The following definition is standard, and found as such in most textbooks on formal language theory.
24
25
Given a finite
alphabet
Σ, the following constants are defined
as regular expressions:
empty set
) ∅ denoting the set ∅.
empty string
) ε denoting the set containing only the "empty" string, which has no characters at all.
literal character
in Σ denoting the set containing only the character
Given regular expressions R and S, the following operations over them are defined
to produce regular expressions:
concatenation
(RS)
denotes the set of strings that can be obtained by concatenating a string accepted by R and a string accepted by S (in that order). For example, let R denote {"ab", "c"} and S denote {"d", "ef"}. Then,
(RS)
denotes {"abd", "abef", "cd", "cef"}.
alternation
(R|S)
denotes the
set union
of sets described by R and S. For example, if R describes {"ab", "c"} and S describes {"ab", "d", "ef"}, expression
(R|S)
describes {"ab", "c", "d", "ef"}.
Kleene star
(R*)
denotes the smallest
superset
of the set described by
that contains ε and is
closed
under string concatenation. This is the set of all strings that can be made by concatenating any finite number (including zero) of strings from the set described by R. For example, if R denotes {"0", "1"},
(R*)
denotes the set of all finite
binary strings
(including the empty string). If R denotes {"ab", "c"},
(R*)
denotes {ε, "ab", "c", "abab", "abc", "cab", "cc", "ababab", "abcab", ...}.
To avoid parentheses, it is assumed that the Kleene star has the highest priority followed by concatenation, then alternation. If there is no ambiguity, then parentheses may be omitted. For example,
(ab)c
can be written as
abc
, and
a|(b(c*))
can be written as
a|bc*
. Many textbooks use the symbols ∪, +, or ∨ for alternation instead of the vertical bar.
Examples:
a|b*
denotes {ε, "a", "b", "bb", "bbb", ...}
(a|b)*
denotes the set of all strings with no symbols other than "a" and "b", including the empty string: {ε, "a", "b", "aa", "ab", "ba", "bb", "aaa", ...}
ab*(c|ε)
denotes the set of strings starting with "a", then zero or more "b"s and finally optionally a "c": {"a", "ac", "ab", "abc", "abb", "abbc", ...}
(0|(1(01*0)*1))*
denotes the set of binary numbers that are multiples of 3: { ε, "0", "00", "11", "000", "011", "110", "0000", "0011", "0110", "1001", "1100", "1111", "00000", ...}
The derivative of a regular expression can be defined using the
Brzozowski derivative
Expressive power and compactness
edit
The formal definition of regular expressions is minimal on purpose, and avoids defining
and
—these can be expressed as follows:
a+
aa*
, and
a?
(a|ε)
. Sometimes the
complement
operator is added, to give a
generalized regular expression
; here
matches all strings over Σ* that do not match
. In principle, the complement operator is redundant, because it does not grant any more expressive power. However, it can make a regular expression much more concise—eliminating a single complement operator can cause a
double exponential
blow-up of its length.
26
27
28
Regular expressions in this sense can express the regular languages, exactly the class of languages accepted by
deterministic finite automata
. There is, however, a significant difference in compactness. Some classes of regular languages can only be described by deterministic finite automata whose size grows
exponentially
in the size of the shortest equivalent regular expressions. The standard example here is the languages
consisting of all strings over the alphabet {
} whose
th-from-last letter equals
. On the one hand, a regular expression describing
is given by
{\displaystyle (a\mid b)^{*}a(a\mid b)(a\mid b)(a\mid b)}
Generalizing this pattern to
gives the expression:
times
{\displaystyle (a\mid b)^{*}a\underbrace {(a\mid b)(a\mid b)\cdots (a\mid b)} _{k-1{\text{ times}}}.\,}
On the other hand, it is known that every deterministic finite automaton accepting the language
must have at least 2
states. Luckily, there is a simple mapping from regular expressions to the more general
nondeterministic finite automata
(NFAs) that does not lead to such a blowup in size; for this reason NFAs are often used as alternative representations of regular languages. NFAs are a simple variation of the type-3
grammars
of the
Chomsky hierarchy
24
In the opposite direction, there are many languages easily described by a DFA that are not easily described by a regular expression. For instance, determining the validity of a given
ISBN
requires computing the remainder of an integer modulo 11, and can be easily implemented with an 11-state DFA. However, converting it to a regular expression results in a 2.14-megabyte file.
29
Given a regular expression,
Thompson's construction algorithm
computes an equivalent nondeterministic finite automaton. A conversion in the opposite direction is achieved by
Kleene's algorithm
Finally, many real-world "regular expression" engines implement features that cannot be described by the regular expressions in the sense of formal language theory; rather, they implement
regexes
. See
below
for more on this.
Deciding equivalence of regular expressions
edit
As seen in many of the examples above, there is more than one way to construct a regular expression to achieve the same results.
It is possible to write an
algorithm
that, for two given regular expressions, decides whether the described languages are equal; the algorithm reduces each expression to a
minimal deterministic finite state machine
, and determines whether they are
isomorphic
(equivalent).
Algebraic laws for regular expressions can be obtained using a method by Gischer which is best explained along an example: In order to check whether (
and (
denote the same regular language, for all regular expressions
, it is necessary and sufficient to check whether the particular regular expressions (
and (
denote the same language over the alphabet Σ={
}. More generally, an equation
between regular-expression terms with variables holds if, and only if, its instantiation with different variables replaced by different symbol constants holds.
30
31
Every regular expression can be written solely in terms of the
Kleene star
and
set unions
over finite words. This is a surprisingly difficult problem. As simple as the regular expressions are, there is no method to systematically rewrite them to some normal form. The lack of axiom in the past led to the
star height problem
. In 1991,
Dexter Kozen
axiomatized regular expressions as a
Kleene algebra
, using equational and
Horn clause
axioms.
32
Already in 1964, Redko had proved that no finite set of purely equational axioms can characterize the algebra of regular languages.
33
Syntax
edit
A regex
pattern
matches a target
string
. The pattern is composed of a sequence of
atoms
. An atom is a single point within the regex pattern which it tries to match to the target string. The simplest atom is a literal, but grouping parts of the pattern to match an atom will require using
( )
as metacharacters. Metacharacters help form:
atoms
quantifiers
telling how many atoms (and whether it is a
greedy
quantifier
or not); a logical OR character, which offers a set of alternatives, and a logical NOT character, which negates an atom's existence; and backreferences to refer to previous atoms of a completing pattern of atoms. A match is made, not when all the atoms of the string are matched, but rather when all the pattern atoms in the regex have matched. The idea is to make a small pattern of characters stand for a large number of possible strings, rather than compiling a large list of all the literal possibilities.
Depending on the regex processor there are about fourteen metacharacters, characters that may or may not have their
literal
character meaning, depending on context, or whether they are "escaped", i.e. preceded by an
escape sequence
, in this case, the backslash
. Modern and POSIX extended regexes use metacharacters more often than their literal meaning, so to avoid "backslash-osis" or
leaning toothpick syndrome
, they have a metacharacter escape to a literal mode; starting out, however, they instead have the four bracketing metacharacters
( )
and
{ }
be primarily literal, and "escape" this usual meaning to become metacharacters. Common standards implement both. The usual metacharacters are
{}[]()^$.|*+?
and
. The usual characters that become metacharacters when escaped are
dswDSW
and
Delimiters
edit
When entering a regex in a programming language, they may be represented as a usual string literal, hence usually quoted; this is common in C, Java, and Python for instance, where the regex
re
is entered as
"re"
. However, they are often written with slashes as
delimiters
, as in
/re/
for the regex
re
. This originates in
ed
, where
is the editor command for searching, and an expression
/re/
can be used to specify a range of lines (matching the pattern), which can be combined with other commands on either side, most famously
g/re/p
as in
grep
("global regex print"), which is included in most
Unix
-based operating systems, such as
Linux
distributions. A similar convention is used in
sed
, where search and replace is given by
s/re/replacement/
and patterns can be joined with a comma to specify a range of lines as in
/re1/,/re2/
. This notation is particularly well known due to its use in
Perl
, where it forms part of the syntax distinct from normal string literals. In some cases, such as sed and Perl, alternative delimiters can be used to avoid collision with contents, and to avoid having to escape occurrences of the delimiter character in the contents. For example, in sed the command
s,/,X,
will replace a
with an
, using commas as delimiters.
IEEE POSIX Standard
edit
The
IEEE
POSIX
standard has three sets of compliance:
BRE
(Basic Regular Expressions),
34
ERE
(Extended Regular Expressions), and
SRE
(Simple Regular Expressions). SRE is
deprecated
35
in favor of BRE, as both provide
backward compatibility
. The subsection below covering the
character classes
applies to both BRE and ERE.
BRE and ERE work together. ERE adds
, and
, and it removes the need to escape the metacharacters
( )
and
{ }
, which are
required
in BRE. Furthermore, as long as the POSIX standard syntax for regexes is adhered to, there can be, and often is, additional syntax to serve specific (yet POSIX compliant) applications. Although POSIX.2 leaves some implementation specifics undefined, BRE and ERE provide a "standard" which has since been adopted as the default syntax of many tools, where the choice of BRE or ERE modes is usually a supported option. For example,
GNU
grep
has the following options: "
grep -E
" for ERE, and "
grep -G
" for BRE (the default), and "
grep -P
" for
Perl
regexes.
Perl regexes have become a de facto standard, having a rich and powerful set of atomic expressions. Perl has no "basic" or "extended" levels. As in POSIX EREs,
( )
and
{ }
are treated as metacharacters unless escaped; other metacharacters are known to be literal or symbolic based on context alone. Additional functionality includes
lazy matching
backreferences
, named capture groups, and
recursive
patterns.
POSIX basic and extended
edit
In the
POSIX
standard, Basic Regular Syntax (
BRE
) requires that the
metacharacters
( )
and
{ }
be designated
\(\)
and
\{\}
, whereas Extended Regular Syntax (
ERE
) does not.
Metacharacter
Description
Matches the starting position within the string. In line-based tools, it matches the starting position of any line.
Matches any single character (many applications exclude
newlines
, and exactly which characters are considered newlines is flavor-, character-encoding-, and platform-specific, but it is safe to assume that the line feed character is included). Within POSIX bracket expressions, the dot character matches a literal dot. For example,
a.c
matches "abc", etc., but
[a.c]
matches only "a", ".", or "c".
[ ]
A bracket expression. Matches a single character that is contained within the brackets. For example,
[abc]
matches "a", "b", or "c".
[a-z]
specifies a range which matches any lowercase letter from "a" to "z". These forms can be mixed:
[abcx-z]
matches "a", "b", "c", "x", "y", or "z", as does
[a-cx-z]
The
character is treated as a literal character if it is the last or the first (after the
, if present) character within the brackets:
[abc-]
[-abc]
[^-abc]
. Backslash escapes are not allowed. The
character can be included in a bracket expression if it is the first (after the
, if present) character:
[]abc]
[^]abc]
[^ ]
Matches a single character that is not contained within the brackets. For example,
[^abc]
matches any character other than "a", "b", or "c".
[^a-z]
matches any single character that is not a lowercase letter from "a" to "z". Likewise, literal characters and ranges can be mixed.
Matches the ending position of the string or the position just before a string-ending newline. In line-based tools, it matches the ending position of any line.
( )
Defines a marked subexpression, also called a capturing group, which is essential for extracting the desired part of the text (See also the next entry,
).
BRE mode requires
\( \)
Matches what the
th marked subexpression matched, where
is a digit from 1 to 9. This construct is defined in the POSIX standard.
36
Some tools allow referencing more than nine capturing groups. Also known as a back-reference, this feature is supported in BRE mode.
Matches the preceding element zero or more times. For example,
ab*c
matches "ac", "abc", "abbbc", etc.
[xyz]*
matches "", "x", "y", "z", "zx", "zyx", "xyzzy", and so on.
(ab)*
matches "", "ab", "abab", "ababab", and so on.
Matches the preceding element at least
and not more than
times. For example,
a{3,5}
matches only "aaa", "aaaa", and "aaaaa". This is not found in a few older instances of regexes. BRE mode requires
\{
Examples:
.at
matches any three-character string ending with "at", including "hat", "cat", "bat", "4at", "#at" and " at" (starting with a space).
[hc]at
matches "hat" and "cat".
[^b]at
matches all strings matched by
.at
except "bat".
[^hc]at
matches all strings matched by
.at
other than "hat" and "cat".
^[hc]at
matches "hat" and "cat", but only at the beginning of the string or line.
[hc]at$
matches "hat" and "cat", but only at the end of the string or line.
\[.\]
matches any single character surrounded by "[" and "]" since the brackets are escaped, for example: "[a]", "[b]", "[7]", "[@]", "[]]", and "[ ]" (bracket space bracket).
s.*
matches s followed by zero or more characters, for example: "s", "saw", "seed", "s3w96.7", and "s6#h%(>>>m n mQ".
According to Russ Cox, the POSIX specification requires ambiguous subexpressions to be handled in a way different from Perl's. The committee replaced Perl's rules with one that is simple to explain, but the new "simple" rules are actually more complex to implement: they were incompatible with pre-existing tooling and made it essentially impossible to define a "lazy match" (see below) extension. As a result, very few programs actually implement the POSIX subexpression rules (even when they implement other parts of the POSIX syntax).
37
Metacharacters in POSIX extended
edit
The meaning of metacharacters
escaped
with a backslash is reversed for some characters in the POSIX Extended Regular Expression (
ERE
) syntax. With this syntax, a backslash causes the metacharacter to be treated as a literal character. So, for example,
\( \)
is now
( )
and
\{ \}
is now
{ }
. Additionally, support is removed for
backreferences and the following metacharacters are added:
Metacharacter
Description
Matches the preceding element zero or one time. For example,
ab?c
matches only "ac" or "abc".
Matches the preceding element one or more times. For example,
ab+c
matches "abc", "abbc", "abbbc", and so on, but not "ac".
The choice (also known as alternation or set union) operator matches either the expression before or the expression after the operator. For example,
abc|def
matches "abc" or "def".
Examples:
[hc]?at
matches "at", "hat", and "cat".
[hc]*at
matches "at", "hat", "cat", "hhat", "chat", "hcat", "cchchat", and so on.
[hc]+at
matches "hat", "cat", "hhat", "chat", "hcat", "cchchat", and so on, but not "at".
cat|dog
matches "cat" or "dog".
POSIX Extended Regular Expressions can often be used with modern Unix utilities by including the
command line
flag
-E
Character classes
edit
The character class is the most basic regex concept after a literal match. It makes one small sequence of characters match a larger set of characters. For example,
[A-Z]
could stand for any uppercase letter in the English alphabet, and
could mean any digit. Character classes apply to both POSIX levels.
When specifying a range of characters, such as
[a-Z]
(i.e. lowercase
to uppercase
), the computer's locale settings determine the contents by the numeric ordering of the character encoding. They could store digits in that sequence, or the ordering could be
abc...zABC...Z
, or
aAbBcC...zZ
. So the POSIX standard defines a character class, which will be known by the regex processor installed. Those definitions are in the following table:
Description
POSIX
Perl/Tcl
Vim
Java
ASCII
ASCII characters
ASCII
[\x00-\x7F]
Alphanumeric characters
[:alnum:]
Alnum
[A-Za-z0-9]
Alphanumeric characters plus "_"
[A-Za-z0-9_]
Non-word characters
[^A-Za-z0-9_]
Alphabetic characters
[:alpha:]
Alpha
[A-Za-z]
Space and tab
[:blank:]
Blank
[ \t]
Word boundaries
\< \>
(?
)(?=
)|(?
)(?=
Non-word boundaries
(?
)(?=
)|(?
)(?=
Control characters
[:cntrl:]
Cntrl
[\x00-\x1F\x7F]
Digits
[:digit:]
Digit
or
[0-9]
Non-digits
[^0-9]
Visible characters
[:graph:]
Graph
[\x21-\x7E]
Lowercase letters
[:lower:]
Lower
[a-z]
Visible characters and the space character
[:print:]
[\x20-\x7E]
Punctuation characters
[:punct:]
Punct
[][!"#$%&'()*+,./:;<=>?@\^_`{|}~-]
Whitespace characters
[:space:]
_s
Space
or
\t
\r
\n
\v
\f
Non-whitespace characters
[^ \t\r\n\v\f]
Uppercase letters
[:upper:]
Upper
[A-Z]
Hexadecimal digits
[:xdigit:]
XDigit
[A-Fa-f0-9]
POSIX character classes can only be used within bracket expressions. For example,
[[:upper:]
ab
matches the uppercase letters and lowercase "a" and "b".
An additional non-POSIX class understood by some tools is
[:word:]
, which is usually defined as
[:alnum:]
plus underscore. This reflects the fact that in many programming languages these are the characters that may be used in identifiers. The editor
Vim
further distinguishes
word
and
word-head
classes (using the notation
and
) since in many programming languages the characters that can begin an identifier are not the same as those that can occur in other positions: numbers are generally excluded, so an identifier would look like
or
[[:alpha:]
[[:alnum:]
in POSIX notation.
Note that what the POSIX regex standards call
character classes
are commonly referred to as
POSIX character classes
in other regex flavors which support them. With most other regex flavors, the term
character class
is used to describe what POSIX calls
bracket expressions
Perl and PCRE
edit
See also:
Perl Compatible Regular Expressions
Because of its expressive power and (relative) ease of reading, many other utilities and programming languages have adopted syntax similar to
Perl
's—for example,
Java
JavaScript
Julia
Python
Ruby
Qt
, Microsoft's
.NET Framework
, and
XML Schema
. Some languages and tools such as
Boost
and
PHP
support multiple regex flavors. Perl-derivative regex implementations are not identical and usually implement a subset of features found in Perl 5.0, released in 1994. Perl sometimes does incorporate features initially found in other languages. For example, Perl 5.10 implements syntactic extensions originally developed in PCRE and Python.
38
Lazy matching
edit
In Python and some other implementations (e.g. Java), the three common quantifiers (
, and
) are
greedy
by default because they match as many characters as possible.
39
The regex
".+"
(including the double-quotes) applied to the string
"Ganymede," he continued, "is the largest moon in the Solar System."
matches the entire line (because the entire line begins and ends with a double-quote) instead of matching only the first part,
"Ganymede,"
. The aforementioned quantifiers may, however, be made
lazy
or
minimal
or
reluctant
, matching as few characters as possible, by appending a question mark:
".+?"
matches only
"Ganymede,"
39
Possessive matching
edit
In Java and Python 3.11+,
40
quantifiers may be made
possessive
by appending a plus sign, which disables backing off (in a backtracking engine), even if doing so would allow the overall match to succeed:
41
While the regex
".*"
applied to the string
"Ganymede," he continued, "is the largest moon in the Solar System."
matches the entire line, the regex
".*+"
does
not match at all
, because
.*+
consumes the entire input, including the final
. Thus, possessive quantifiers are most useful with negated character classes, e.g.
"[^"]*+"
, which matches
"Ganymede,"
when applied to the same string.
Another common extension serving the same function is atomic grouping, which disables backtracking for a parenthesized group. The typical syntax is
(?>group)
. For example, while
^(wi|w)i$
matches both
wi
and
wii
^(?>wi|w)i$
only matches
wii
because the engine is forbidden from backtracking and so cannot try setting the group to "w" after matching "wi".
42
Possessive quantifiers are easier to implement than greedy and lazy quantifiers, and are typically more efficient at runtime.
41
IETF I-Regexp
edit
IETF RFC 9485 describes "I-Regexp: An Interoperable Regular Expression Format". It specifies a limited subset of regular-expression idioms designed to be interoperable, i.e. produce the same effect, in a large number of regular-expression libraries. I-Regexp is also limited to matching, i.e. providing a true or false match between a regular expression and a given piece of text. Thus, it lacks advanced features such as capture groups, lookahead, and backreferences.
43
Patterns for non-regular languages
edit
Many features found in virtually all modern regular expression libraries provide an expressive power that exceeds the
regular languages
. For example, many implementations allow grouping subexpressions with parentheses and recalling the value they match in the same expression (
backreferences
). This means that, among other things, a pattern can match strings of repeated words like "papa" or "WikiWiki", called
squares
in formal language theory. The pattern for these strings is
(.+)\1
The language of squares is not regular, nor is it
context-free
, due to the
pumping lemma
. However,
pattern matching
with an unbounded number of backreferences, as supported by numerous modern tools, is still
context sensitive
44
The general problem of matching any number of backreferences is
NP-complete
, and the execution time for known algorithms grows exponentially by the number of backreference groups used.
45
However, many tools, libraries, and engines that provide such constructions still use the term
regular expression
for their patterns. This has led to a nomenclature where the term regular expression has different meanings in
formal language theory
and pattern matching. For this reason, some people have taken to using the term
regex
regexp
, or simply
pattern
to describe the latter.
Larry Wall
, author of the Perl programming language, writes in an essay about the design of Raku:
"Regular expressions" […] are only marginally related to real regular expressions. Nevertheless, the term has grown with the capabilities of our pattern matching engines, so I'm not going to try to fight linguistic necessity here. I will, however, generally call them "regexes" (or "regexen", when I'm in an Anglo-Saxon mood).
19
Assertions
edit
Assertion
Lookbehind
Lookahead
Positive
(?
<=
pattern
(?
pattern
Negative
(?
pattern
(?
pattern
Lookbehind and lookahead assertions
in
Perl
regular expressions
Other features not found in describing regular languages include assertions. These include the ubiquitous
and
, used since at least 1970,
46
as well as some more sophisticated extensions like lookaround that appeared in 1994.
47
Lookarounds define the surrounding of a match and do not spill into the match itself, a feature only relevant for the use case of string searching.
citation needed
Some of them can be simulated in a regular language by treating the surroundings as a part of the language as well.
48
The
look-ahead assertions
(?=...)
and
(?!...)
have been attested since at least 1994, starting with Perl 5.
47
The lookbehind assertions
(?<=...)
and
(?are attested since 1997 in a commit by Ilya Zakharevich to Perl 5.005.
49
Implementations and running times
edit
There are at least three different
algorithms
that decide whether and how a given regex matches a string.
The oldest and fastest relies on a result in formal language theory that allows every
nondeterministic finite automaton
(NFA) to be transformed into a
deterministic finite automaton
(DFA). The DFA can be constructed explicitly and then run on the resulting input string one symbol at a time. Constructing the DFA for a regular expression of size
has the time and memory cost of
(2
), but it can be run on a string of size
in time
). Note that the size of the expression is the size after abbreviations, such as numeric quantifiers, have been expanded.
An alternative approach is to simulate the NFA directly, essentially building each DFA state on demand and then discarding it at the next step. This keeps the DFA implicit and avoids the exponential construction cost, but running cost rises to
mn
). The explicit approach is called the DFA algorithm and the implicit approach the NFA algorithm. Adding caching to the NFA algorithm is often called the "lazy DFA" algorithm, or just the DFA algorithm without making a distinction. These algorithms are fast, but using them for recalling grouped subexpressions, lazy quantification, and similar features is tricky.
50
51
Modern implementations include the re1-
re2
-sregex family based on Cox's code.
The third algorithm is to match the pattern against the input string by
backtracking
. This algorithm is commonly called NFA, but this terminology can be confusing. Its running time can be exponential, which simple implementations exhibit when matching against expressions like
aa
that contain both alternation and unbounded quantification and force the algorithm to consider an exponentially increasing number of sub-cases. This behavior can cause a security problem called
Regular expression Denial of Service
(ReDoS).
Although backtracking implementations only give an exponential guarantee in the worst case, they provide much greater flexibility and expressive power. For example, any implementation which allows the use of backreferences, or implements the various extensions introduced by Perl, must include some kind of backtracking. Some implementations try to provide the best of both algorithms by first running a fast DFA algorithm, and revert to a potentially slower backtracking algorithm only when a backreference is encountered during the match. GNU grep (and the underlying gnulib DFA) uses such a strategy.
52
Sublinear runtime algorithms have been achieved using
Boyer-Moore (BM) based algorithms
and related DFA optimization techniques such as the reverse scan.
53
GNU grep, which supports a wide variety of POSIX syntaxes and extensions, uses BM for a first-pass prefiltering, and then uses an implicit DFA. Wu
agrep
, which implements approximate matching, combines the prefiltering into the DFA in BDM (backward DAWG matching). NR-grep's BNDM extends the BDM technique with Shift-Or bit-level parallelism.
54
A few theoretical alternatives to backtracking for backreferences exist, and their "exponents" are tamer in that they are only related to the number of backreferences, a fixed property of some regexp languages such as POSIX. One naive method that duplicates a non-backtracking NFA for each backreference note has a complexity of
{\displaystyle {\mathrm {O} }(n^{2k+2})}
time and
{\displaystyle {\mathrm {O} }(n^{2k+1})}
space for a haystack of length n and k backreferences in the RegExp.
55
Theoretical work based on memory automata gives a tighter bound based on "active" variable nodes used, and a polynomial possibility for some backreferenced regexps.
56
Unicode
edit
In theoretical terms, any token set can be matched by regular expressions as long as it is pre-defined. In terms of historical implementations, regexes were originally written to use
ASCII
characters as their token set though regex libraries have supported numerous other
character sets
. Many modern regex engines offer at least some support for
Unicode
. In most respects it makes no difference what the character set is, but some issues do arise when extending regexes to support Unicode.
Supported encoding
. Some regex libraries expect to work on some particular encoding instead of on abstract Unicode characters. Many of these require the
UTF-8
encoding, while others might expect
UTF-16
, or
UTF-32
. In contrast, Perl and Java are agnostic on encodings, instead operating on decoded characters internally.
Supported Unicode range
. Many regex engines support only the
Basic Multilingual Plane
, that is, the characters which can be encoded with only 16 bits. Currently (as of 2016
[update]
) only a few regex engines (e.g., Perl's and Java's) can handle the full 21-bit Unicode range.
Extending ASCII-oriented constructs to Unicode
. For example, in ASCII-based implementations, character ranges of the form
[x-y]
are valid wherever
and
have
code points
in the range [0x00,0x7F] and codepoint(
) ≤ codepoint(
). The natural extension of such character ranges to Unicode would simply change the requirement that the endpoints lie in [0x00,0x7F] to the requirement that they lie in [0x0000,0x10FFFF]. However, in practice this is often not the case. Some implementations, such as that of
gawk
, do not allow character ranges to cross Unicode blocks. A range like [0x61,0x7F] is valid since both endpoints fall within the Basic Latin block, as is [0x0530,0x0560] since both endpoints fall within the Armenian block, but a range like [0x0061,0x0532] is invalid since it includes multiple Unicode blocks. Other engines, such as that of the
Vim
editor, allow block-crossing but the character values must not be more than 256 apart.
57
Case insensitivity
. Some case-insensitivity flags affect only the ASCII characters. Other flags affect all characters. Some engines have two different flags, one for ASCII, the other for Unicode. Exactly which characters belong to the POSIX classes also varies.
Cousins of case insensitivity
. As ASCII has case distinction, case insensitivity became a logical feature in text searching. Unicode introduced alphabetic scripts without case like
Devanagari
. For these,
case sensitivity
is not applicable. For scripts like Chinese, another distinction seems logical: between traditional and simplified. In Arabic scripts, insensitivity to
initial, medial, final, and isolated position
may be desired. In Japanese, insensitivity between
hiragana
and
katakana
is sometimes useful.
Normalization
. Unicode has
combining characters
. Like old typewriters, plain base characters (white spaces, punctuation characters, symbols, digits, or letters) can be followed by one or more non-spacing symbols (usually diacritics, like accent marks modifying letters) to form a single printable character; but Unicode also provides a limited set of precomposed characters, i.e. characters that already include one or more combining characters. A sequence of a base character + combining characters should be matched with the identical single precomposed character (only some of these combining sequences can be precomposed into a single Unicode character, but infinitely many other combining sequences are possible in Unicode, and needed for various languages, using one or more combining characters after an initial base character; these combining sequences
may
include a base character or combining characters partially precomposed, but not necessarily in canonical order and not necessarily using the canonical precompositions). The process of standardizing sequences of a base character + combining characters by decomposing these
canonically equivalent
sequences, before reordering them into canonical order (and optionally recomposing
some
combining characters into the leading base character) is called normalization.
New control codes
. Unicode introduced, among other codes,
byte order marks
and text direction markers. These codes might have to be dealt with in a special way.
Introduction of character classes for Unicode blocks, scripts, and numerous other character properties
. Block properties are much less useful than script properties, because a block can have code points from several different scripts, and a script can have code points from several different blocks.
58
In
Perl
and the
java.util.regex
library, properties of the form
\p{InX}
or
\p{Block=X}
match characters in block
and
\P{InX}
or
\P{Block=X}
matches code points not in that block. Similarly,
\p{Armenian}
\p{IsArmenian}
, or
\p{Script=Armenian}
matches any character in the Armenian script. In general,
\p{X}
matches any character with either the binary property
or the general category
. For example,
\p{Lu}
\p{Uppercase_Letter}
, or
\p{GC=Lu}
matches any uppercase letter. Binary properties that are
not
general categories include
\p{White_Space}
\p{Alphabetic}
\p{Math}
, and
\p{Dash}
. Examples of non-binary properties are
\p{Bidi_Class=Right_to_Left}
\p{Word_Break=A_Letter}
, and
\p{Numeric_Value=10}
Language support
edit
Main article:
Comparison of regular expression engines
Most
general-purpose programming languages
support regex capabilities, either natively or via
libraries
Uses
edit
This section
needs additional citations for
verification
Please help
improve this article
by
adding citations to reliable sources
in this section. Unsourced material may be challenged and removed.
January 2025
Learn how and when to remove this message
Regexes are useful in a wide variety of text processing tasks, and more generally
string processing
, where the data need not be textual. Common applications include
data validation
data scraping
(especially
web scraping
),
data wrangling
, simple
parsing
, the production of
syntax highlighting
systems, and many other tasks.
Some high-end
desktop publishing
software has the ability to use regexes to automatically apply text styling, saving the person doing the layout from laboriously doing this by hand for anything that can be matched by a regex. For example, by defining a
character style
that makes text into
small caps
and then using the regex
[A-Z]{4,}
to apply that style, any word of four or more consecutive capital letters will be automatically rendered as small caps instead.
While regexes would be useful on Internet
search engines
, processing them across the entire database could consume excessive computer resources depending on the complexity and design of the regex. Although in many cases system administrators can run regex-based queries internally, most search engines do not offer regex support to the public. Notable exceptions include
Google Code Search
and
Exalead
. However, Google Code Search was shut down in January 2012.
59
Examples
edit
The specific syntax rules vary depending on the specific implementation,
programming language
, or
library
in use. Additionally, the functionality of regex implementations can vary between
versions
Because regexes can be difficult to both explain and understand without examples, interactive websites for testing regexes are a useful resource for learning regexes by experimentation.
This section provides a basic description of some of the properties of regexes by way of illustration.
The following conventions are used in the examples.
60
metacharacter(s) ;; the metacharacters column specifies the regex syntax being demonstrated
=~ m//  ;; indicates a regex
match
operation in Perl
=~ s///  ;; indicates a regex
substitution
operation in Perl
These regexes are all Perl-like syntax. Standard
POSIX
regular expressions are different.
Unless otherwise indicated, the following examples conform to the
Perl
programming language, release 5.8.8, January 31, 2006. This means that other implementations may lack support for some parts of the syntax shown here (e.g. basic vs. extended regex,
\( \)
vs.
()
, or lack of
\d
instead of
POSIX
[:digit:]
).
The syntax and conventions used in these examples coincide with that of other programming environments as well.
61
Meta­character(s)
Description
Example
62
Normally matches any character except a newline.
Within square brackets the dot is literal.
$string1
"Hello World\n"
if
$string1
=~
m/...../
"$string1 has length >= 5.\n"
Output:
Hello World
has length >= 5.
( )
Groups a series of pattern elements to a single element.
When you match a pattern within parentheses, you can use any of
$1
$2
, ... later to refer to the previously matched pattern. Some implementations may use a backslash notation instead, like
\1
\2
$string1
"Hello World\n"
if
$string1
=~
m/(H..).(o..)/
"We matched '$1' and '$2'.\n"
Output:
We matched 'Hel' and 'o W'.
Matches the preceding pattern element one or more times.
$string1
"Hello World\n"
if
$string1
=~
m/l+/
"There are one or more consecutive letter \"l\"'s in $string1.\n"
Output:
There are one or more consecutive letter "l"'s in Hello World.
Matches the preceding pattern element zero or one time.
$string1
"Hello World\n"
if
$string1
=~
m/H.?e/
"There is an 'H' and a 'e' separated by "
"0-1 characters (e.g., He Hue Hee).\n"
Output:
There is an 'H' and a 'e' separated by 0-1 characters (e.g., He Hue Hee).
Modifies the
or
{M,N}
'd regex that comes before to match as few times as possible.
$string1
"Hello World\n"
if
$string1
=~
m/(l.+?o)/
"The non-greedy match with 'l' followed by one or "
"more characters is 'llo' rather than 'llo Wo'.\n"
Output:
The non-greedy match with 'l' followed by one or more characters is 'llo' rather than 'llo Wo'.
Matches the preceding pattern element zero or more times.
$string1
"Hello World\n"
if
$string1
=~
m/el*o/
"There is an 'e' followed by zero to many "
"'l' followed by 'o' (e.g., eo, elo, ello, elllo).\n"
Output:
There is an 'e' followed by zero to many 'l' followed by 'o' (e.g., eo, elo, ello, elllo).
{M,N}
Denotes the minimum M and the maximum N match count.
N can be omitted and M can be 0:
{M}
matches "exactly" M times;
{M,}
matches "at least" M times;
{0,N}
matches "at most" N times.
x* y+ z?
is thus equivalent to
x{0,} y{1,} z{0,1}
$string1
"Hello World\n"
if
$string1
=~
m/l{1,2}/
"There exists a substring with at least 1 "
"and at most 2 l's in $string1\n"
Output:
There exists a substring with at least 1 and at most 2 l's in Hello World
[…]
Denotes a set of possible character matches.
$string1
"Hello World\n"
if
$string1
=~
m/[aeiou]+/
"$string1 contains one or more vowels.\n"
Output:
Hello World
contains one or more vowels.
Separates alternate possibilities.
$string1
"Hello World\n"
if
$string1
=~
m/(Hello|Hi|Pogo)/
"$string1 contains at least one of Hello, Hi, or Pogo."
Output:
Hello World
contains at least one of Hello, Hi, or Pogo.
\b
Matches a zero-width boundary between a word-class character (see next) and either a non-word class character or an edge; same as
(^\w|\w$|\W\w|\w\W)
$string1
"Hello World\n"
if
$string1
=~
m/llo\b/
"There is a word that ends with 'llo'.\n"
Output:
There is a word that ends with 'llo'.
\w
Matches an alphanumeric character, including "_";
same as
[A-Za-z0-9_]
in ASCII, and
[\p{Alphabetic}
\p{GC=Mark}
\p{GC=Decimal_Number}
\p{GC=Connector_Punctuation}]
in Unicode,
58
where the
Alphabetic
property contains more than Latin letters, and the
Decimal_Number
property contains more than Arab digits.
$string1
"Hello World\n"
if
$string1
=~
m/\w/
"There is at least one alphanumeric "
"character in $string1 (A-Z, a-z, 0-9, _).\n"
Output:
There is at least one alphanumeric character in Hello World
(A-Z, a-z, 0-9, _).
\W
Matches a
non
-alphanumeric character, excluding "_";
same as
[^A-Za-z0-9_]
in ASCII, and
[^\p{Alphabetic}
\p{GC=Mark}
\p{GC=Decimal_Number}
\p{GC=Connector_Punctuation}]
in Unicode.
$string1
"Hello World\n"
if
$string1
=~
m/\W/
"The space between Hello and "
"World is not alphanumeric.\n"
Output:
The space between Hello and World is not alphanumeric.
\s
Matches a whitespace character,
which in ASCII are tab, line feed, form feed, carriage return, and space;
in Unicode, also matches no-
break spaces, next line, and the variable-
width spaces (among others).
$string1
"Hello World\n"
if
$string1
=~
m/\s.*\s/
"In $string1 there are TWO whitespace characters, which may"
" be separated by other characters.\n"
Output:
In Hello World
there are TWO whitespace characters, which may be separated by other characters.
\S
Matches anything
but
a whitespace.
$string1
"Hello World\n"
if
$string1
=~
m/\S.*\S/
"In $string1 there are TWO non-whitespace characters, which"
" may be separated by other characters.\n"
Output:
In Hello World
there are TWO non-whitespace characters, which may be separated by other characters.
\d
Matches a digit;
same as
[0-9]
in ASCII;
in Unicode, same as the
\p{Digit}
or
\p{GC=Decimal_Number}
property, which itself the same as the
\p{Numeric_Type=Decimal}
property.
$string1
"99 bottles of beer on the wall."
if
$string1
=~
m/(\d+)/
"$1 is the first number in '$string1'\n"
Output:
99 is the first number in '99 bottles of beer on the wall.'
\D
Matches a non-digit;
same as
[^0-9]
in ASCII or
\P{Digit}
in Unicode.
$string1
"Hello World\n"
if
$string1
=~
m/\D/
"At least one character in $string1"
" is not a digit.\n"
Output:
At least one character in Hello World
is not a digit.
Matches the beginning of a line or string.
$string1
"Hello World\n"
if
$string1
=~
m/^He/
"$string1 starts with the characters 'He'.\n"
Output:
Hello World
starts with the characters 'He'.
Matches the end of a line or string.
$string1
"Hello World\n"
if
$string1
=~
m/rld$/
"$string1 is a line or string "
"that ends with 'rld'.\n"
Output:
Hello World
is a line or string that ends with 'rld'.
\A
Matches the beginning of a string (but not an internal line).
$string1
"Hello\nWorld\n"
if
$string1
=~
m/\AH/
"$string1 is a string "
"that starts with 'H'.\n"
Output:
Hello
World
is a string that starts with 'H'.
\z
Matches the end of a string (but not an internal line).
63
$string1
"Hello\nWorld\n"
if
$string1
=~
m/d\n\z/
"$string1 is a string "
"that ends with 'd\\n'.\n"
Output:
Hello
World
is a string that ends with 'd\n'.
[^…]
Matches every character except the ones inside brackets.
$string1
"Hello World\n"
if
$string1
=~
m/[^abc]/
"$string1 contains a character other than "
"a, b, and c.\n"
Output:
Hello World
contains a character other than a, b, and c.
Induction
edit
Main article:
Induction of regular languages
Regular expressions can often be created ("induced" or "learned") based on a set of example strings. This is known as the
induction of regular languages
and is part of the general problem of
grammar induction
in
computational learning theory
. Formally, given examples of strings in a regular language, and perhaps also given examples of strings
not
in that regular language, it is possible to induce a grammar for the language, i.e., a regular expression that generates that language. Not all regular languages can be induced in this way (see
language identification in the limit
), but many can. For example, the set of examples {1, 10, 100}, and negative set (of counterexamples) {11, 1001, 101, 0} can be used to induce the regular expression 1⋅0* (1 followed by zero or more 0s).
See also
edit
Comparison of regular expression engines
Extended Backus–Naur form
Matching wildcards
Regular tree grammar
Thompson's construction
– converts a regular expression into an equivalent
nondeterministic finite automaton (NFA)
Notes
edit
Goyvaerts, Jan.
"Regular Expression Tutorial - Learn How to Use Regular Expressions"
Regular-Expressions.info
Archived
from the original on 2016-11-01
. Retrieved
2016-10-31
Mitkov, Ruslan (2003).
The Oxford Handbook of Computational Linguistics
. Oxford University Press. p. 754.
ISBN
978-0-19-927634-9
Archived
from the original on 2017-02-28
. Retrieved
2016-07-25
Lawson, Mark V. (17 September 2003).
Finite Automata
. CRC Press. pp.
98–
100.
ISBN
978-1-58488-255-8
Archived
from the original on 27 February 2017
. Retrieved
25 July
2016
"How a Regex Engine Works Internally"
regular-expressions.info
. Retrieved
24 February
2024
Heddings, Anthony (11 March 2020).
"How Do You Actually Use Regex?"
howtogeek.com
. Retrieved
24 February
2024
Kleene 1951
Leung, Hing (16 September 2010).
"Regular Languages and Finite Automata"
(PDF)
New Mexico State University
. Archived from
the original
(PDF)
on 5 December 2013
. Retrieved
13 August
2019
The concept of regular events was introduced by Kleene via the definition of regular expressions.
Kleene 1951,
pg46
Thompson 1968
Johnson et al. 1968
Kernighan, Brian
(2007-08-08).
"A Regular Expressions Matcher"
Beautiful Code
O'Reilly Media
. pp.
1–
2.
ISBN
978-0-596-51004-6
Archived
from the original on 2020-10-07
. Retrieved
2013-05-15
Ritchie, Dennis M.
"An incomplete history of the QED Text Editor"
. Archived from
the original
on 1999-02-21
. Retrieved
9 October
2013
Aho & Ullman 1992
, 10.11 Bibliographic Notes for Chapter 10, p. 589.
Aycock 2003
, p. 98.
Raymond, Eric S.
citing
Dennis Ritchie
(2003).
"Jargon File 4.4.7: grep"
. Archived from
the original
on 2011-06-05
. Retrieved
2009-02-17
"New Regular Expression Features in Tcl 8.1"
Archived
from the original on 2020-10-07
. Retrieved
2013-10-11
"Documentation: 9.3: Pattern Matching"
PostgreSQL
Archived
from the original on 2020-10-07
. Retrieved
2013-10-12
Wall, Larry
(2006).
"Perl Regular Expressions"
perlre
Archived
from the original on 2009-12-31
. Retrieved
2006-10-10
Wall (2002)
"PCRE - Perl Compatible Regular Expressions"
www.pcre.org
. Retrieved
2024-04-07
"GRegex – Faster Analytics for Unstructured Text Data"
grovf.com
. Archived from
the original
on 2020-10-07
. Retrieved
2026-04-20
"CUDA grep"
bkase.github.io
Archived
from the original on 2020-10-07
. Retrieved
2019-10-22
Kerrisk, Michael.
"grep(1) - Linux manual page"
man7.org
. Retrieved
31 January
2023
Hopcroft, Motwani & Ullman (2000)
Sipser (1998)
Gelade & Neven (2008
, p. 332, Thm.4.1)
Gruber & Holzer (2008)
Based on
Gelade & Neven (2008)
, a regular expression of length about 850 such that its complement has a length about 2
32
can be found at
File:RegexComplementBlowup.png
"Regular expressions for deciding divisibility"
s3.boskent.com
. Retrieved
2024-02-21
Gischer, Jay L. (1984). (Title unknown) (Technical Report). Stanford Univ., Dept. of Comp. Sc.
title missing
Hopcroft, John E.; Motwani, Rajeev & Ullman, Jeffrey D. (2003).
Introduction to Automata Theory, Languages, and Computation
. Upper Saddle River, New Jersey: Addison Wesley. pp.
117–
120.
ISBN
978-0-201-44124-6
This property need not hold for extended regular expressions, even if they describe no larger class than regular languages; cf. p.121.
Kozen (1991)
page needed
Redko, V.N. (1964).
"On defining relations for the algebra of regular events"
Ukrainskii Matematicheskii Zhurnal
(in Russian).
16
(1):
120–
126.
Archived
from the original on 2018-03-29
. Retrieved
2018-03-28
ISO/IEC 9945-2:1993
Information technology – Portable Operating System Interface (POSIX) – Part 2: Shell and Utilities
, successively revised as ISO/IEC 9945-2:2002
Information technology – Portable Operating System Interface (POSIX) – Part 2: System Interfaces
, ISO/IEC 9945-2:2003, and currently ISO/IEC/IEEE 9945:2009
Information technology – Portable Operating System Interface (POSIX) Base Specifications, Issue 7
The Single Unix Specification (Version 2)
"9.3.6 BREs Matching Multiple Characters"
The Open Group Base Specifications Issue 7, 2018 edition
. The Open Group. 2017
. Retrieved
December 10,
2023
Russ Cox (2009).
"Regular Expression Matching: the Virtual Machine Approach"
swtch.com
Digression: POSIX Submatching
"Perl Regular Expression Documentation"
. perldoc.perl.org.
Archived
from the original on December 31, 2009
. Retrieved
November 5,
2024
"Regular Expression Syntax"
Python 3.5.0 documentation
Python Software Foundation
. Archived from
the original
on 18 July 2018
. Retrieved
10 October
2015
SRE: Atomic Grouping (?>...) is not supported #34627
"Essential classes: Regular Expressions: Quantifiers: Differences Among Greedy, Reluctant, and Possessive Quantifiers"
The Java Tutorials
Oracle
Archived
from the original on 7 October 2020
. Retrieved
23 December
2016
"Atomic Grouping"
Regex Tutorial
Archived
from the original on 7 October 2020
. Retrieved
24 November
2019
Bormann, Carsten; Bray, Tim.
I-Regexp: An Interoperable Regular Expression Format
. Internet Engineering Task Force.
doi
10.17487/RFC9485
RFC
9485
. Retrieved
11 March
2024
Cezar Câmpeanu; Kai Salomaa & Sheng Yu (Dec 2003).
"A Formal Study of Practical Regular Expressions"
International Journal of Foundations of Computer Science
14
(6):
1007–
1018.
doi
10.1142/S012905410300214X
Archived
from the original on 2015-07-04
. Retrieved
2015-07-03
Theorem 3 (p.9)
"Perl Regular Expression Matching is NP-Hard"
perl.plover.com
Archived
from the original on 2020-10-07
. Retrieved
2019-11-21
Ritchie, D. M.; Thompson, K. L. (June 1970).
QED Text Editor
(PDF)
. MM-70-1373-3. Archived from
the original
(PDF)
on 2015-02-03
. Retrieved
2022-09-05
Reprinted as "QED Text Editor Reference Manual", MHCC-004, Murray Hill Computing, Bell Laboratories (October 1972).
Wall, Larry (1994-10-18).
"Perl 5: perlre.pod"
GitHub
Wandering Logic.
"How to simulate lookaheads and lookbehinds in finite state automata?"
Computer Science Stack Exchange
Archived
from the original on 7 October 2020
. Retrieved
24 November
2019
Zakharevich, Ilya (1997-11-19).
"Jumbo Regexp Patch Applied (with Minor Fix-Up Tweaks): Perl/perl5@c277df4"
GitHub
Cox (2007)
Laurikari (2009)
"gnulib/lib/dfa.c"
. Archived from
the original
on 2021-08-18
. Retrieved
2022-02-12
If the scanner detects a transition on backref, it returns a kind of "semi-success" indicating that the match will have to be verified with a backtracking matcher.
Kearns, Steven (August 2013). "Sublinear Matching With Finite Automata Using Reverse Suffix Scanning".
arXiv
1308.3822
cs.DS
].
Navarro, Gonzalo (10 November 2001).
"NR-grep: a fast and flexible pattern-matching tool"
(PDF)
Software: Practice and Experience
31
(13):
1265–
1312.
doi
10.1002/spe.411
S2CID
3175806
Archived
(PDF)
from the original on 7 October 2020
. Retrieved
21 November
2019
"travisdowns/polyregex"
GitHub
. 5 July 2019.
Archived
from the original on 14 September 2020
. Retrieved
21 November
2019
Schmid, Markus L. (March 2019). "Regular Expressions with Backreferences: Polynomial-Time Matching Techniques".
arXiv
1903.05896
cs.FL
].
"Vim documentation: pattern"
. Vimdoc.sourceforge.net.
Archived
from the original on 2020-10-07
. Retrieved
2013-09-25
"UTS#18 on Unicode Regular Expressions, Annex A: Character Blocks"
Archived
from the original on 2020-10-07
. Retrieved
2010-02-05
Horowitz, Bradley
(24 October 2011).
"A fall sweep"
Google Blog
Archived
from the original on 21 October 2018
. Retrieved
4 May
2019
The character 'm' is not always required to specify a
Perl
match operation. For example,
m/[^abc]/
could also be rendered as
/[^abc]/
. The 'm' is only necessary if the user wishes to specify a match operation without using a forward-slash as the regex
delimiter
. Sometimes it is useful to specify an alternate regex delimiter in order to avoid "
delimiter collision
". See '
perldoc perlre
Archived
2009-12-31 at the
Wayback Machine
' for more details.
E.g., see
Java
in a Nutshell
, p. 213;
Python
Scripting for Computational Science
, p. 320; Programming
PHP
, p. 106.
All the if statements return a TRUE value
Conway, Damian
(2005).
"Regular Expressions, End of String"
Perl Best Practices
O'Reilly
. p. 240.
ISBN
978-0-596-00173-5
Archived
from the original on 2020-10-07
. Retrieved
2017-09-10
References
edit
Aho, Alfred V.
(1990). "Algorithms for finding patterns in strings". In
van Leeuwen, Jan
(ed.).
Handbook of Theoretical Computer Science, volume A: Algorithms and Complexity
. The MIT Press. pp.
255–
300.
Aho, Alfred V.;
Ullman, Jeffrey D.
(1992).
"Chapter 10. Patterns, Automata, and Regular Expressions"
(PDF)
Foundations of Computer Science
Archived
from the original on 2020-10-07
. Retrieved
2013-12-14
Aycock, John (June 2003).
"A brief history of just-in-time"
(PDF)
ACM Computing Surveys
35
(2):
97–
113.
CiteSeerX
10.1.1.97.3985
doi
10.1145/857076.857077
S2CID
15345671
"Regular Expressions".
The Single UNIX Specification, Version 2
. The Open Group. 1997.
Archived
from the original on 2020-10-07
. Retrieved
2011-12-13
"Chapter 9: Regular Expressions"
The Open Group Base Specifications
(6). The Open Group. 2004. IEEE Std 1003.1, 2004 Edition.
Archived
from the original on 2011-12-02
. Retrieved
2011-12-13
Cox, Russ (2007).
"Regular Expression Matching Can Be Simple and Fast"
. Archived from
the original
on 2010-01-01
. Retrieved
2008-04-27
Forta, Ben
(2004).
Sams Teach Yourself Regular Expressions in 10 Minutes
. Sams.
ISBN
978-0-672-32566-3
Friedl, Jeffrey E. F. (2002).
Mastering Regular Expressions
O'Reilly
ISBN
978-0-596-00289-3
Archived
from the original on 2005-08-30
. Retrieved
2005-04-26
Gelade, Wouter; Neven, Frank (2008).
Succinctness of the Complement and Intersection of Regular Expressions
Proceedings of the 25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008)
. pp.
325–
336.
arXiv
0802.2869
. Archived from
the original
on 2011-07-18
. Retrieved
2009-06-15
Goyvaerts, Jan; Levithan, Steven (2009).
Regular Expressions Cookbook
. [O'reilly].
ISBN
978-0-596-52068-7
Gruber, Hermann; Holzer, Markus (2008).
Finite Automata, Digraph Connectivity, and Regular Expression Size
(PDF)
Proceedings of the 35th International Colloquium on Automata, Languages and Programming (ICALP 2008)
. Lecture Notes in Computer Science. Vol. 5126. pp.
39–
50.
doi
10.1007/978-3-540-70583-3_4
ISBN
978-3-540-70582-6
Archived
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. Retrieved
2011-02-03
Habibi, Mehran (2004).
Real World Regular Expressions with Java 1.4
. Springer.
ISBN
978-1-59059-107-9
Hopcroft, John E.; Motwani, Rajeev; Ullman, Jeffrey D. (2000).
Introduction to Automata Theory, Languages, and Computation
(2nd ed.). Addison-Wesley.
Johnson, Walter L.; Porter, James H.; Ackley, Stephanie I.; Ross, Douglas T. (1968).
"Automatic generation of efficient lexical processors using finite state techniques"
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Kleene, Stephen C. (1951). "Representation of Events in Nerve Nets and Finite Automata". In Shannon, Claude E.; McCarthy, John (eds.).
Automata Studies
(PDF)
. Princeton University Press. pp.
3–
42.
Archived
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. Retrieved
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Kozen, Dexter (1991). "A completeness theorem for Kleene algebras and the algebra of regular events".
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"TRE library 0.7.6"
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Stubblebine, Tony (2003).
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Archived
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External links
edit
Wikibooks has a book on the topic of:
Regular Expressions
The Wikibook
R Programming
has a page on the topic of:
Text Processing
Look up
regular expression
in Wiktionary, the free dictionary.
Media related to
Regex
at Wikimedia Commons
ISO/IEC/IEEE 9945:2009
Information technology – Portable Operating System Interface (POSIX) Base Specifications, Issue 7
Regular Expressions, IEEE Std 1003.1-2024, Open Group
Open source list of regular expression resources
Automata theory
formal languages
and
formal grammars
Chomsky hierarchy
Grammars
Languages
Abstract machines
Type-0
Type-1
Type-2
Type-3
Unrestricted
(no common name)
Context-sensitive
Positive
range concatenation
Indexed
Linear context-free rewriting systems
Tree-adjoining
Context-free
Deterministic context-free
Visibly pushdown
Regular
Non-recursive
Recursively enumerable
Decidable
Context-sensitive
Positive
range concatenation
Indexed
Linear context-free rewriting language
Tree-adjoining
Context-free
Deterministic context-free
Visibly pushdown
Regular
Star-free
Finite
Turing machine
Decider
Linear-bounded
PTIME
Turing Machine
Nested stack
Thread automaton
restricted
Tree stack automaton
Embedded pushdown
Nondeterministic pushdown
Deterministic pushdown
Visibly pushdown
Finite
Counter-free (with aperiodic finite monoid)
Acyclic finite
Each category of languages, except those marked by a
, is a
proper subset
of the category directly above it.
Any language in each category is generated by a grammar and by an automaton in the category in the same line.
Strings
String metric
Approximate string matching
Bitap algorithm
Damerau–Levenshtein distance
Edit distance
Gestalt pattern matching
Hamming distance
Jaro–Winkler distance
Lee distance
Levenshtein automaton
Levenshtein distance
Wagner–Fischer algorithm
String-searching algorithm
Apostolico–Giancarlo algorithm
Boyer–Moore string-search algorithm
Boyer–Moore–Horspool algorithm
Knuth–Morris–Pratt algorithm
Rabin–Karp algorithm
Raita algorithm
Trigram search
Two-way string-matching algorithm
Zhu–Takaoka string matching algorithm
Multiple string searching
Aho–Corasick
Commentz-Walter algorithm
Regular expression
Comparison of regular-expression engines
Regular grammar
Thompson's construction
Nondeterministic finite automaton
Sequence alignment
BLAST
Hirschberg's algorithm
Needleman–Wunsch algorithm
Smith–Waterman algorithm
Data structure
DAFSA
Substring index
Suffix array
Suffix automaton
Suffix tree
Compressed suffix array
LCP array
FM-index
Generalized suffix tree
Rope
Ternary search tree
Trie
Other
Parsing
Pattern matching
Compressed pattern matching
Longest common subsequence
Longest common substring
Sequential pattern mining
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String rewriting systems
String operations
Authority control databases
International
GND
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United States
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Yale LUX
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