Abstract
The paper develops the theory of Turing machines as recognizers of infinite (ω-type) input tapes. Various models of ω-type Turing acceptors are considered, varying mainly in their mechanism for recognizing ω-tapes. A comparative study of the models is made. It is shown that regardless of the ω-recognition model considered, non-deterministic ω-Turing acceptors are strictly more powerful than their deterministic counterparts. Canonical forms are obtained for each of the ω-Turing acceptor models. The corresponding families of ω-sets are studied; normal forms and algebraic characterizations are derived for each family.
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