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CIE
2007
Springer

The Complexity of Quickly ORM-Decidable Sets

9 years 3 months ago
The Complexity of Quickly ORM-Decidable Sets
Abstract. 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 ωω . Further, we show that the hyperarithmetical sets are exactly those sets that can be decided by an ORM in time uniformly less than ωCK 1 . Key words: Ordinal, ordinal computation, infinite time computation, computability, register machine, arithmetical hierarchy, hyperarithmetical hierarchy, complexity
Joel David Hamkins, David Linetsky, Russell G. Mil
Added 07 Jun 2010
Updated 07 Jun 2010
Type Conference
Year 2007
Where CIE
Authors Joel David Hamkins, David Linetsky, Russell G. Miller
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