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$$\infty$$-regular languages defined by a limit operator. (English) Zbl 0857.68070
Summary: Finite deterministic $$\infty$$-acceptor accepting both finite and infinite words over a finite alphabet is introduced. It is shown that $$\infty$$-regular languages can be defined as sets of $$\infty$$-words accepted by an $$\infty$$-acceptor. A limit operator on regular languages is used to define a special class of $$\infty$$-regular languages. In $$\infty$$-acceptors accepting these languages incidence relations between the sets used for acceptance are determined.
##### MSC:
 68Q45 Formal languages and automata
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