Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Higher recursion theory
Recursion theory
An Enhanced Theory of Infinite Time Register Machines
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
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The Ordinal Register Machine (ORM) is one of several different machine models for infinitary computability. We classify, by complexity, the sets that can be decided quickly by ORMs. In particular, we show that the arithmetical sets are exactly those sets that can be decided by ORMs in times uniformly less than ${\ensuremath{\omega^\omega}}$. Further, we show that the hyperarithmetical sets are exactly those sets that can be decided by an ORM in time uniformly less than $\omega_1^{CK}$.