Powers of Sigma

A notation to describe a Language in terms of the length of Strings that can be created from a given Alphabet

Definition

• Given $\Sigma$ as the Alphabet
• ${\Sigma }^n=\{\text{set of all strings length n from }\Sigma \}$

Example

• $\Sigma =\{0,1\}$
• ${\Sigma }^0=\varnothing$
• ${\Sigma }^1=\{0,1\}$
• ${\Sigma }^2=\{00,01,10,11\}$
• …