Regular Language & Expressions

Regular Language A regular language is one that a finite state machine (fsm) will accept. ‘Alphabet’: {a, b} ‘Rules’: {a(a | b)* Example strings: {“a”, “aa”, “ab”, “aab”, “abb”.. } Note: | - OR * - zero or more instances

Regular Language & Expressions Non-regular Language To construct a language that is non-regular a language must be created that has an infinite number of states.

Regular Language & Expressions Regular expressions A basic and important computing task is to try to manipulate different strings. Example: To search for the word ‘cat’ in a large section of text (eg “catching a cold”) To search for a specific pattern in a person’s DNA (Pattern matching)

Regular Language & Expressions Regular expressions Sometimes a set of rules need to be checked to verify accuracy. Example: Checking an address -One or more lowercase letters followed symbol -One or more lowercase letters followed by. Symbol -One or more lowercase letters followed by.co then.uk

Regular Language & Expressions Regular expressions notation The notation below represents a regular expression, regex or pattern. ‘Alphabet’: {a, b} ‘Rules’: {a(a | b)* Example strings: {“a”, “aa”, “ab”, “aab”, “abb”.. } (This describes an infinite set, without listing all the members of the set)

Regular Language & Expressions Regular expressions notation Example: ‘Alphabet’: {a - z} ‘Strings’: {“michel”, “michael”, “michell”) What rule represents the following strings represented above? {Mich (e | ae | el) l}

Regular Language & Expressions Regular expressions notation Here are some regular expressions that are defined by The formal expression {a, b} a is a regular expression that matches a string consisting of just a b is a regular expression that matches a string consisting of just b ab is a regular expression that matches a string consisting of the symbol a followed by the symbol b a* is a regular expression that matches a string consisting of zero or more a’s a+ is a regular expression that matches a string consisting of one or more a’s

Regular Language & Expressions Regular expressions notation Here are some regular expressions that are defined by The formal expression {a, b} abb? is a regular expression that matches the string ab or the string abb The symbol ‘?’ indicates there is a zero or one of the preceding element. a | b is a regular expression that matches a string consisting of the symbol a or consisting of the symbol b.

Regular Language & Expressions Regular expression Now we will take a look at some examples.

Regular Language & Expressions Regular expression Examples of strings: abc defines the language with one string, “abc” abc | bac defines the language with two strings, “abc” and “bac” a+ defines the language with the strings, “a”, “aa”, “aaa”, “aaaa” ab* defines the language with the strings, “ab”, “abb”, “abbb”, “abbbb” (ac)* defines the language with the strings, “ ”, “ac”, “acac”, “acacac”, “acacacac”

Regular Language & Expressions Regular expression Examples of strings: a*ca*ca defines the language withany number of a’s, but exactly two c’s (a | c)* defines the language that describes any possible combination of a and c, including the empty string

Regular Language & Expressions Regular expression Meta characters Vertical bar (pipe character) | Question mark ? Asterisk (star) * Plus sign + Both round brackets ( ) Both square brackets [ ] The backslash character \

Regular Language & Expressions Regular expression Meta characters Caret Dollar sign $ Period or dot. Hyphen -

Regular Language & Expressions Regular expression ‘Alternatives’ A vertical bar represents alternatives: a | b represents a or b. Searching through a series of words in a paragraph this might bring up either: ban bed

Regular Language & Expressions Regular expression ‘Character Class’ An alternative way of expressing alternation uses square brackets [] (eg [ab] means a or b). The usual expression b [ae] d matches: bed bad b [ae] d acts as the list of alternatives