Substring

Definition

A string $x$ is a substring of $y$ if:

• There exists strings $x^{\prime },x^{\prime \prime }$ (They could be Empty String)
• $x^{\prime }x{x}^{\prime \prime }=y$ A Proper Substring is a type of substring

Empty String Substring

The number of substrings ${\#}_{ϵ}(x)=|x|+1$