Conference Paper

Quantitative Aspects of Speed-Up and Gap Phenomena.

DOI: 10.1017/S0960129510000174 Conference: Theory and Applications of Models of Computation, 6th Annual Conference, TAMC 2009, Changsha, China, May 18-22, 2009. Proceedings
Source: DBLP

ABSTRACT 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 which 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 the nonspeedable problems does not have effective measure 0 too. These results answer some questions raised
by Calude and Zimand in [CZ96] and [Zim06]. We also give a short quantitative analysis of Borodin and Trakhtenbrot’s Gap Theorem
which corrects a claim in [CZ96] and [Zim06].

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