Sequence Strings

Strings

A finite sequence of elements. Given set $A$, we can construct the set $A^{\ast }$ (string over $A$), consisting of all finite sequences of elements of $A$.

Example

$A=\{x\mid x\text{ is a letter in the English alphabet }\}$

$A^{\ast }$ consists of all ordinary words, whether they have meaning or not.

Order

Unlike sets, the order in which the elements in the string is written is important.

Example

$\text{Let }X=\{a,b,c\}baac\ne acabbbaaac=b^2{a}^{3}c$

Length

The length of a string $\alpha$ is the number of elements in $\alpha$, denoted by $|\alpha |$.

Example

$\alpha =aabab|\alpha |=5$

$\beta =a^3{b}^4{a}^{3}2|\beta |=39$

Null String

A string with no elements, denoted by $\lambda$ (also called empty string).