Regular Expressions

Theory

A regular expression is a series of characters that define a search pattern.

• a formal language is a set of strings of symbols that may be constrained by rules
  • the alphabet of a formal language is the (often finite) set of symbols and letters that can form strings
  • in complexity theory, decision problems are formal languages and complexity classes are sets of formal languages
• a regular language is a formal language that can be expressed with regular expressions
  • many formal languages cannot be expressed as regular expressions

In Practice

• Start with ^ and end with $ to match the whole string to the regex.
• Since usually trying to match for a string S, not find substring R in S, we use the /^regex$/ method to apply it to the whole string
• regex{3,} will match three or more times
• \b is a word boundary (before first \w in matched string, between a \w and \W, after last \w)
  - /\bis\b/ would match "This is cool", not "This is cool" because it needs to start at a word boundary
• ? after any quantifier (*?, {1,5}? etc...) is Lazy quantifier (no ? is called greedy). Lazy matches as few as possible
• () capturing and (?: ) non-capturing used to group part of the regex and apply quantifiers.
• \1, \2 match the first and second capturing groups again (references). (\w)(\w)\w\2\1 will match any 5 letter palindrome
• backreferencing to a capturing group that matches nothing is different from backreferencing to a capturing group that did not participate in the match.
  - Matches nothing: (b?)o\1 matches "o" where b? matches nothing so \1 doesn't either
  - Doesn't participate: (b)?o\1 fails to match "o" for most flavors (except JavaScript). (b) is optional, o matches, \1 references a group that did not participate so backreference fails (\1 has nothing to reference).
• Fowardreferencing is using backreferences before grouping, and it is evaluated after the group is matched.
• Branch reset groups (?|regex) is used to choose on from multiple possible capturing groups and assigns it to one given group number
  • (x)(?|(a)|(bc)|(def))\2 matches xaa, xbcbc, or xdefdef, each assigned to number 2

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