Abstract
We analyze the fine structure of the time complexity classes induced by random access machines. Say that A and B have the same time complexity (A+ C B) if for all time constructible f A ∈ DTIME RAM (f) ⇔ B ∈ DTIME RAM (f). The = C -equivalence class of A is called it complexity type. We examine the set theoretic relationships between the sets in an arbitrary complexity type C. For example, every recursive set X can be partitioned into two sets A and B such that A = C B = C X. Additionally, the ordering of C under ⊂* (inclusion modulo finite sets) is dense.
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© 1992 Springer-Verlag New York, Inc
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Maass, W., Slaman, T.A. (1992). Splitting and Density for the Recursive Sets of a Fixed Time Complexity. In: Moschovakis, Y.N. (eds) Logic from Computer Science. Mathematical Sciences Research Institute Publications, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2822-6_14
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DOI: https://doi.org/10.1007/978-1-4612-2822-6_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7685-2
Online ISBN: 978-1-4612-2822-6
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