Examples of Regular Grammars and Regular Expressions

Ex. 2:
Find a regular expression corresponding to the language of all strings over the alphabet { a, b } that contain exactly two a's.

Solution:
A string in this language must have at least two a's. Since any string of b's can be placed in front of the first a, behind the second a and between the two a's, and since an arbitrasry string of b's can be represented by the regular expression b*, b*a b*a b* is a regular expression for this language.


Ex. 3:
Find a regular expression corresponding to the language of all strings over the alphabet { a, b } that do not end with ab.

Solution:
Any string in a language over { a , b } must end in a or b. Hence if a string does not end with ab then it ends with a or if it ends with b the last b must be preceded by a symbol b. Since it can have any string in front of the last a or bb, ( a + b )*( a + bb ) is a regular expression for the language

Automata Step by Step

Today, we will discuss “Regular expressions”.

Regular expressions:

A regular expression (also "RegEx" or "regex”) is a string that is used to describe or match a set of strings, according to certain syntax rules. 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

In another words, a regular expression, often called a pattern, is an expression that describes a set of strings. They are usually used to give a concise description of a set, without having to list all elements. For example, the set containing the three strings Handel, Händel, and Haendel can be described by the pattern "H(ä|ae?)ndel" (or alternatively, it is said that the pattern matches each of the three strings). In most formalism, if there is any regex that matches a particular set then there are an infinite number of such expressions.