Regular Expressions
A regular expression is a notation for defining all the valid strings of a formal language.
Contents
Examples of Regular Expression Notation
| Regular Expression | Meaning |
|---|---|
| a | Matches a string consisting of just the symbol a |
| b | Matches a string consisting of just the symbol b |
| ab | Matches a string consisting of the symbol a followed by the symbol b |
| a* | Matches a string consisting of zero or more a’s |
| a+ | Matches a string consisting of one or more a’s |
| abb? | Matches the string ab or the string abb. The ? symbol indicates zero or one of the preceding element |
| a|b | Matches a string consisting of the symbol a or the symbol b |
Precedence Rules
When using regular expressions, the rules of arithmetic precedence are as follows:
+ and * are done first
Concatenation (ie joining elements together) is done next
| comes last
More Examples
Examples of regular expressions using the alphabet {a, b, c}
- abc defines the language with only the string ‘abc’
- abc | cba defines the language with two strings’ abc’ and ‘cba’
- (a | b) c (a | b) gives four strings: ‘aca’, ‘acb’, ‘bca’, ‘bcb’
- a+ gives an infinite number of strings: ‘a’, ‘aa’, ‘aaa’, etc
- ab* gives an infinite number of strings: ‘a’, ‘ab’, ‘abb’, ‘abbb’, etc
- (ab)* gives an infinite number of strings: ‘’, ‘ab’, ‘abab’, ‘ababab’, etc
- (a | c)+ gives all possible strings of a and c (not including the empty string)
Regular expression meta-characters
Symbol Meaning Example │ Used to separate alternatives a│b Means a or b ? Used to denote zero or one of the preceding element a? 0 or 1 as; matches with ‘’ & ‘a’
- Used to denote zero or more of the preceding element a*
0 or more as; matches with ‘’, ‘a’, ‘aa’, etc. + Used to denote one or more of the preceding element a+ 1 or more as; matches with ‘a’, ‘aa”’etc. ( ) Used to group characters together, to indicate the scope of another operator (ab)* 0 or more abs; matches with ‘’, ‘ab’, ‘abab’, etc. [ ] Another way of denoting alternatives (instead of vertical bar). Defines a character class [ab] means a or b \ The escape character (this turns the metacharacter into an ordinary character) a\* the a character followed by the * character. Note: \ is needed as a* would mean zero or more as. ^ Used to indicate the negation of a character class
Also used to match the position before the first character in a string a[^bc] a followed by a character that is not a b or c ^abc will match with abc only if it is at the beginning of a string $ Used to match with the position after the last character in a string abc$ will match with abc only if it is at the end of a string . Matches with any single character a.a will match with any string that has an a followed by any character followed by an a e.g. ‘aca’, ‘aba’ - Used to specify a range of values in a character class [A-Z] character in the range of A to Z
