What is Regular Expression

Q. What is Regular Expression ?

Ans. The language accepted by finite automata can be easily described by simple expressions called Regular Expressions.
Σ denote input set.

1. Φ is a regular expression which denotes the empty set. 
2. ε is a regular expression and denotes the set {ε} and it is a null string. 
3. For each ‘a’ in  Σ  ‘a’ is a regular expression and denotes the set (a). 
4. If R1 and R2 are regular expressions denoting the Languages L1 and L2 respectively, then 
  • R1+R2 is equivalent to LI ∪ L2 i.e. union. 
  • R1R2 is equivalent to L1 ∩  L2 i.e. concatenation 
  • R* is equivalent to L1* i.e. closure. 
The R* is known as kleen closure or closure which indicates occurrence of R for infinite number of times. 
Some other examples of regular expressions:
  1. R = a*, ie. all combinations of a.
  2. R = a+, ie. all combinations of a without null string.
  3. R = (a+b)*, ie. strings containg any number of a and b