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JSYML
2006

Degrees of monotone complexity

13 years 3 months ago
Degrees of monotone complexity
Levin and Schnorr (independently) introduced the monotone complexity, Km(), of a binary string . We use monotone complexity to define the relative complexity (or relative randomness) of reals. We define a partial ordering Km on 2 by Km iff there is a constant c such that Km( n) Km( n) + c for all n. The monotone degree of is the set of all such that Km and Km . We show the monotone degrees contain an antichain of size 20 , a countable dense linear ordering (of degrees of cardinality 20 ), and a minimal pair. Downey, Hirschfeldt, LaForte, Nies and others have studied a similar structure, the Kdegrees, where K is the prefix-free Kolmogorov complexity. A minimal pair of K-degrees was constructed by Csima and Montalb
William C. Calhoun
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where JSYML
Authors William C. Calhoun
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