ω-regular language

Definition

• if A is a nonempty regular language not containing the empty string, then $A^{\omega }$ is a ω-regular language
• if A is a regular language, B is a ω-regular language, then AB is a ω-regular language
• if $A_i$ ‘s are ω-regular language, then ${\bigcup }_{i=1}^n{A}_i$ is a ω-regular language.

ω-regular language generalized the definition of regular language to ω-language.

Equivalence

It is equivalent to nondertermistic Büchi automata and monadic second-order logic (S1S).