Abstract
The decision time of an infinite time algorithm is the supremum of its halting times over all real inputs. The decision time of a set of reals is the least decision time of an algorithm that decides the set; semidecision times of semidecidable sets are defined similarly. It is not hard to see that is the maximal decision time of sets of reals. Our main results determine the supremum of countable decision times as σ and that of countable semidecision times as τ, where σ and τ denote the suprema of - and -definable ordinals, respectively, over . We further compute analogous suprema for singletons.
Citation
Merlin Carl. Philipp Schlicht. Philip Welch. "Decision Times of Infinite Computations." Notre Dame J. Formal Logic 63 (2) 197 - 212, May 2022. https://doi.org/10.1215/00294527-2022-0012
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