The Free On-line Dictionary of Computing (30 December 2018):

regular expression
RE

   1.  (regexp, RE) One of the wild
   card patterns used by Perl and other languages, following
   Unix utilities such as grep, sed, and awk and editors
   such as vi and Emacs.  Regular expressions use conventions
   similar to but more elaborate than those described under
   glob.  A regular expression is a sequence of characters with
   the following meanings (in Perl, other flavours vary):

   An ordinary character (not one of the special characters
   discussed below) matches that character.

   A backslash (\) followed by any special character matches the
   special character itself.  The special characters are:

   "." matches any character except newline; "RE*" (where RE is any
   regular expression and the "*" is called the "Kleene star")
   matches zero or more occurrences of RE.  If there is any choice,
   the longest leftmost matching string is chosen.

   "^" at the beginning of an RE matches the start of a line and
   "$" at the end of an RE matches the end of a line.

   [CHARS] matches any one of the characters in CHARS.  If the
   first character of the string is a "^" it matches any
   character except the remaining characters in the string (and
   also usually excluding newline).  "-" may be used to indicate
   a range of consecutive ASCII characters.

   (RE) matches whatever RE matches and \N, where N is a digit,
   matches whatever was matched by the RE between the Nth "(" and
   its corresponding ")" earlier in the same RE.  Many flavours
   use \(RE\) instead of just (RE).

   The concatenation of REs is a RE that matches the
   concatenation of the strings matched by each RE.  RE1 | RE2
   matches whatever RE1 or RE2 matches.

   \< matches the beginning of a word and \> matches the end of a
   word.  Many flavours use "\b" instead as the special character
   for "word boundary".

   RE\M\ matches M occurences of RE.  RE\M,\ matches M or more
   occurences of RE.  RE\M,N\ matches between M and N occurences.
   Other flavours use RE\\M\\ etc.

   Perl provides several "quote-like" operators for writing
   REs, including the common // form and less common ??.

   A comprehensive survey of regexp flavours is found in Friedl
   1997 (see below).

   [Jeffrey E.F. Friedl, "Mastering Regular Expressions
   (http://enterprise.ic.gc.ca/~jfriedl/regex/index.html),
   O'Reilly, 1997].

   2. Any description of a pattern composed from combinations
   of symbols and the three operators:

   Concatenation - pattern A concatenated with B matches a match
   for A followed by a match for B.

   Or - pattern A-or-B matches either a match for A or a match
   for B.

   Closure - zero or more matches for a pattern.

   The earliest form of regular expressions (and the term itself)
   were invented by mathematician Stephen Cole Kleene in the
   mid-1950s, as a notation to easily manipulate "regular sets",
   formal descriptions of the behaviour of finite state
   machines, in regular algebra.

   [S.C. Kleene, "Representation of events in nerve nets and
   finite automata", 1956, Automata Studies. Princeton].

   [J.H. Conway, "Regular algebra and finite machines", 1971, Eds
   Chapman & Hall].

   [Sedgewick, "Algorithms in C", page 294].

   (2015-04-30)