Quantitative aspects of speed-up and gap phenomena
Copyright policy )Quantitative aspects of speed-up and gap phenomena
We show that, for any abstract complexity measure in the sense of Blum and for any computable function f (or computable operator F), the class of problems that are f-speedable (or F-speedable) does not have effective measure 0. On the other hand, for sufficiently fast growing f (or F), the class of non-speedable computable problems does not have effective measure 0. These results answer some questions raised by Calude and Zimand. We also give a quantitative analysis of Borodin and Trakhtenbrot's Gap Theorem, which corrects a claim by Calude and Zimand.
- Heidelberg University Germany
Complexity of computation (including implicit computational complexity), speedable problems, non-speedable problems, computable operator, effective measure, gap theorem, structural complexity theory, effective Baire category, Theory of numerations, effectively presented structures
Complexity of computation (including implicit computational complexity), speedable problems, non-speedable problems, computable operator, effective measure, gap theorem, structural complexity theory, effective Baire category, Theory of numerations, effectively presented structures
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).1 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!